It's a two part question.
1) I don't think any sort of "no Islam" POD affects Britain much until we reach the ATL period corresponding to the First Crusade, around 1100--even then the direct effects of there not being any Crusades at all would not impact a Britain minimally altered from OTL until later centuries than that. Of course overall changes in regional trade patterns would make some generic differences but these would again have more impact on Britain later than earlier I'd think. The main thing the English had to deal with OTL was the Vikings, leading eventually to Normandy existing. Surely with mere butterflies of the chaotic kind it is easy enough to sidestep the Norman Conquest, but in the spirit of "what are the minimal changes required by Islam not existing" that conquest while hardly inevitable is also hardly unlikely for someone on the North Sea (if not Normandy perhaps Flanders?) to attempt anyway.
The reason I doubt a "no Islam" POD affects the far northwest periphery of Europe very much directly is that even without the OTL sweeping loss of the southeast tier of the Eastern Roman Empire (and rapid loss of the southwest as well to become the Maghreb) the ERE is hardly going to be much better able than OTL to project power far to the west, even into Italy let alone beyond. It might seem they could if they hold on to all of North Africa--but the truth is, that even if they proceeded west from the region of Carthage to re-consolidate Mauritania (which would be difficult) their major focus, if "no Islam" means "no conquest of Egypt and the Levant by Arabs," would still be eastward, dealing with a Persia that also presumably does not suffer such conquests of Mesopotamia and indeed OTL their own core territory as well. Now of course of the Arabs are nerfed completely, at any rate as conquerors if not necessarily as rising in importance in their own core region (Red Sea and Indian Ocean trade, maybe expansion along the east African coast) the ERE has more to spare on paper for westward ventures--but by that same token, Persia is also stronger, and even if the ERE retains grip on Egypt and the Levant, whatever benefit they get from that net control has to go largely toward defending at least the Levant, along with Anatolia, and if things go badly for the Romans, perhaps Egypt too, from Persian resurgence.
Now it seems more probable to me that even if Islam doesn't exist, the Arabs are going to assert themselves to some degree more and more around this time and going forward, and that puts Egypt on its own newly vulnerable frontier--the Arabs might well be able to take that region and have possible motives, say if they are adopting some form of Christianity (or a variant on Judaism, but that is getting pretty close to having Islam by another name I suspect--certainly it would clash with OTL Judaism proper much as OTL conflicts with Muslims, which of course were largely resolved OTL by the Jews of the Islamic regions submitting to Islamic authority in return for their Faith of the Book being respected--in a world with a weaker Arabia in more fratricidal ideological conflict with Judaism as we recognize it OTL, this would be less likely to work) to press on to the Levant as well, in fact they are positioned to directly threaten the eastern Med coast and its hinterlands at least as well as Egypt, assuming the Persians aren't in a position to assert control of the region inland from there strongly themselves.
Anyway, Arab expansion toward the Med under any banner, pagan, Christian, a version of Judaism, Buddhist, some variation on Zoroastrian, whatever, brings the overall situation closer to OTL in substance.
A difference might be that northwest Africa is largely left alone--but honestly I think if the Arabs do work their way into running Egypt by any path, their influence will spread westward very rapidly via the northern Sahara just as OTL; perhaps the Moors would adopt whatever religion the Arabs have. It would look more and more like OTL. If the Arabs have adopted some form of Christianity, perhaps the western Latins will tend to ally with them in opposition to the ERE, which would certainly be a major ATL divergence--but even so, while the fates of Italy, Spain and southern France would be much different, I don't see that having much impact north of there.
In short, No Islam strongly affects the Mediterranean world, but not so much north of the Pyrenees/Alps line, except for the enclave of southern France, which is separated by the relatively barren lands of south-central France. Aquitaine would be affected, but not so much to change the general pattern of its relations with peoples further north on the Atlantic.
2) as for general maximal changes, in a sense of course the sky is the limit, as always in ATL. Adopt a strong enough implementation of the Butterfly principle and anything goes after a few hundred years, which is why I think the artistry of AH lies more in looking at deeper currents and being parsimonious with random change just for the hell of it.
Honestly, if we are looking at the Anglo-Saxon realms in particular, until the Vikings started to raid their coasts they were pretty much left alone to develop as they wanted to, and I don't see anyone being in a position to force results much different in general outcome than adopted OTL. Perhaps a Mercian centered evolution might result in a stronger England, but actually even having lost half the land to the Danelaw OTL, Alfred the Great for instance led a pretty strong one OTL, and it is hardly clear to me the Mercians pulling ahead of Wessex would have plausibly been stronger and better able to hold the "Danes" at bay. It all strikes me as six of one, half a dozen of the other, and however we shuffle the Heptarchy cards the general outcome seems likely to be one or two "English" or "Saxon" or whatever we want to call them kingdoms.
BTW, I believe the Angle identity particularly is more in the east and southeast of England, and these people did not dominate the end game of the Heptarchy--the reason the people as a whole, in one kingdom or many of them, are called "Angles" leading to "English" is I think that the Catholic Church dealt with Angles first, and took to calling all the Anglo-Saxon lineage peoples in Britain "Angles" generically--it doesn't relate then to which old Heptarchy core, Wessex, Mercia, Northumbria or someone else even ultimately accomplishes the consolidation, by the time that is in the cards, they've all been calling themselves "English" for some time.
Preventing the Danelaw, or alternatively in the other direction having all the English kingdoms collapse in that invasion and having the politics and culture evolve as a fusion of Nordic and initially pagan conquerors ruling a people I think would cling to Christian identity rather stubbornly and ultimately converting their overlords, seem like the range we have to work with.
No Danelaw at all strikes me as a pretty wankish thing to specify, but not I guess out of bounds of possibility completely--perhaps a situation more like Normandy where a strong English and Christian monarchy (or perhaps several of them--Wessex in the south, Mercia in the west and some Northumbrian remnant in the north maybe) limits the settlement of Nordic invaders, the latter don't unite much politically at all as pagans, but they gradually negotiate some sort of nominally subordinate status as vassals of the Christian kings while de facto having strong autonomy. It might get very interesting if there are two or three rival legacy Christian English kingdoms for neighboring bands of Nordics to play off against each other, perhaps instead establishing their own centralized, more or less, "Danish" kingdom that I do think must ultimately Christianize. Thus this intermediate version of "preventing" the Danelaw by limiting it to smaller than OTL and then "Normandizing" it actually might work out to be a Heptarchy reset, but with most of the separate kingdoms being Christian from the get-go.
A complete collapse of all Anglo-Saxon kingdoms under a wave of Nordic invaders also presents the full spectrum of possibilities, from a deeper Heptarchy reset where the Nordics actually do manage to break the hold of Christianity on the mentality of their subjects resulting in some English fleeing west to Wales to negotiate belatedly with the survivals of the Britons they had overwhelmed as a vast heathen army in their own day while the majority either get killed off or merge with their Nordic invaders culturally and have to be re-Christianized a third time. All the way to the other extreme, whereby loose bands of disparate Nordic invaders pretty much decimate and burn over English institutions, but are also quickly subverted to convert to Christianity, and some ambitious types very quickly consolidate a new kingdom where say at first there are five or six (or Seven! or eight or nine etc of course) enclaves with pretensions of sovereignty, but the majority of these in some zone or other come under one rule (by hook or crook, perhaps not by conquest but by voluntary federation for purposes of more military success) which proceeds to gobble up the rest in fairly short order after that, creating a brand new kingdom that might or might not be called "English" but is fundamentally a variation on unified England of OTL.
In the end I think we go into the eleventh century with things pretty largely as OTL in overall form, regardless of what sorts of detailed ethnic and dynastic zigzags the process of forming the coherent North Germanic stew of a nation would be. And then the question of some kind of conquest from some mainland power is there, but it might be that that was just William getting very lucky OTL and not particularly likely in most TLs. Assuming some sort of strong Continental tie is formed I don't see it being extremely different from OTL in terms of what affects the lives of English people very much; the major alternatives are either No Conquest and ongoing England as a Nordic country, or Some Kinda Conquest and England being tied to Norman or Flemish politics and continental ventures peculiar to the mainland conquerors, with the subjugated English evolving to fuse with their conquerors and make their masters' identity switch over to being lords of the English from among the English rather than conquerors from afar.
Even if the English avoid a Norman or other mainland conquest, and even if they are even more strongly influenced by the Nordics than OTL, I don't see them turning their backs on their neighbors across the Channel completely either. Whoever rules England will be influenced by the interests of lords of England, and will develop ties of some kind with coastal France and Spain and beyond to the Mediterranean, and as the Middle Ages and modern periods develop will be drawn more and more that way and less and less to the north.
