I can't see this changing much. The anglo saxon invaders from across the north sea are still only going to populate the same areas of England as OTL so not much is going to change long term.
I disagree. The main reason Roman Britain broke off from the empire in 410 was because the empire couldn't and wouldn't spare the troops to defend it from the Gaels and the Picts. Without this threat, everything changes.
One, no Hadrian's Wall, which means more cohesiveness through out the island. This seems like a minimal change, but it really means a lot when you consider the raiding tribes who climbed over said wall and lead to...
Two, the Angles, Saxons, and Jutes would not be hired as mercenaries to defend the Romano-Brits against the Gaels and Picts because-- THEY WOULD BE SUBJUGATED!
What's more, if there is never an official break away from the Romans in 410, that means that the island(s) will be less likely to break up into the petty micro-kingdoms it did when the Angles, Saxons, and Jutes invaded. More political unity, plus more man-power from Hibernia and Caledonia means that a possible invasion from these tribes, or similar tribes of similar number, can be rebuffed or held off more affectively. Best case scenario for an invading tribe is that they populate Mercia and Northumbria, possibly Kent. Over the centuries, they would likely become the cultural equivalent to the Welsh in OTL Great Britain/ England before union with Scotland.
Rather than an Anglo-Saxon dominated island, it is more likely that the island be dominated by the Britons. Also, it is unlikely that Pictish will be replaced with Gaelic, because Gaelic colonization of Caledonia will probably be different, and certainly won't result in Gaelic domination of the region.
However, invasion from outside forces does seem inevitable. The Franks may very well invade, but so will the vikings. Will the Norse and/or Danes create their own kingdoms, becoming the Norman analogue?
Also, with the flight of the Angles and Jutes from Juteland, this brings the question of what will occur in Scandinavia? Will the Danes come to prominence, or will the Jutes and/or Angles? How will this affect the political climate of the region. How will having more Saxons in Saxony affect their war with the Franks?
So, IMO, everything changes.