i personally would remove the uk existence from history, even if i have to go all the way back to pangea and sink the whole thing with a manual showel. bonus points because it also prevents burgerland from being born
Are we taking Ireland with that? No real reason it would not become the UK without it, give or take maybe the lack of land compared to the rest of it that could sustain enough of a population to matter (even in current space year with modern tech and a rich scientifically focused country and it is some 6 million on the island of Ireland, compared to the 60 something million in the UK), and variously it was part of it until relatively modern times (can probably just about find someone that remembers it being part of it). Or if you prefer see the religious schisms that formed with Ireland being isolated and doing its own thing, no reason all other politics would not roll that way. If Ireland did carry on then whoever gets their act together on the continent as far as boats gets to use it as a training level instead of the UK, and then a nice place to go cool off when it gets too hot, few more resources and resupply for their wars, then probably a staging ground.
So anyway no big island off the coast of Europe (maybe it went with the rest of
doggerland).
I would wonder at geographical concerns here -- Ireland and the UK being on the end of the gulfstream do act as a bit of a sink, Scandinavia might be a bit warmer and I don't know what goes for the North Sea either. Alternate geography is probably out of the question though as it makes things way too complicated so I will handwave that.
Islands in prehistoric (and even to this day) makes things really hard to invade*; there is a reason longbows were often considered a favoured weapon in the things that would become the UK and part of that was lack of worthwhile opponents on land borders (see the rest of Europe and history thereof) where you get to worry about that as well as peasant uprising.
*D-day landings in the 1940s barely worked and with the industrial might of the US and UK, Russian distraction, bad intel/setup on the part of Germany and practice in Italy (and maybe North Africa) beforehand to work out the kinks. Before that you have what the couple of technical Dutch invasions (the last of which was basically an invite), 1066 (which was also somewhat lucky), a few raids, Danelaw, Hengist and Horsa in the fifth century...
Would the Celts have survived or been a forgotten thing in Northern France, Basques and what goes there, would the Roman empire have stretched itself to that degree or gone another way (England there was not particularly lucrative for them and took a fair bit of resources that could have gone for Germany, Russia, east, south...)?
Europe without the UK playing mediator at various points means it is probably going to be the Germany (I will assume they unite rather than being the source of princes and proxy wars) vs France show, maybe with some fun from the Spanish, Italy is fine for the early game in civilisations but sucks for the later one, Austria-Hungary... hahahaha. Also France without the UK... that is 1000 years change there, if not more if the Saxons decide not to go for the UK (the Normans that did 1066 themselves being vikings that settled there after all) and instead focus other directions. France, England, Scotland, Ireland all pulling all sorts of focus in all sorts of ways here, including the US (war of independence there being influenced by a war with France considerably on various fronts).
Vikings in Asia is also a potentially different story here if there is more reason to make more of a dent there.
No UK for time of empires other than the US (more on that shortly). India would probably have been a French dominion (it was in the early days) as the others were more about trading empires, though maybe the Germans would have got it together to get something. Mughals would likely not have been able to hang on in there.
Would the industrial revolution have kicked off without the UK or would it have been delayed by decades/centuries? Sources of coal and metals are a thing still, a lot of stuff appeared in Germany (de re metallica, something you could happily do quite well with for mining and basic metallurgy, being the 1500s in Germany).
As far as the US appearing. Given it was varyingly vikings, Spanish (who sent an Italian) and more that would have discovered it, with most of the rest of northern Europe in good stead to give it a go (not like Portugal and the Netherlands did not have maritime empires crossing further distances) and go off in search of India. Outside chance of Chinese look into things (see existing US history for timelines here, though I doubt they would have it together to do westward manifest destiny), or maybe Polynesian, Japan was still being isolationist and rarely had a good navy, don't know what goes for Russia here (Alaska was a thing but eh...), Korea potentially an option but again navy a bit lacking and also lack of the north sea to train up on.
Now it adopted UK common law along with some interesting enlightenment/classical liberal concepts rather than French law (which in turn was basically Roman law and similar stories for most of the other possibilities for Europe here) which is a bit of a change. That might be interesting -- whether it would be large Quebec or large New Orleans I don't know, the Spanish and Portuguese might even stick around (doubt the Dutch could have). With the possible exception of the Polynesians then the natives would have been steamrolled by disease either way and then we get massive land grabs, probably followed by a fracture as a 4 months to send ships and weapons means independence probably always going to happen pre steamships and telegraphs. That or it all looks like south America does today (debatable from where I sit as geography influences culture somewhat, especially in pre industrial times).
Take it back 3 billion and piss in the primordial goo. Fuck this disaster. No more Kardashians or robocallers.
Leaving aside questions of panspermia (life arrives on a comet) and likelihood of life evolving independently again or taking hold (the whole thermal vents thing).
The bacteria likely in that (they are the ones that clawed up nature's 3 billion year corpse pile) would potentially do some considerable boosting of evolution if they were able to survive at some level. Even without that the complex proteins there would probably have some fun.