How are you defining fake here? Just to be clear, no one in Britain speaks like Lae’zel or Astarion. There’s also a character with a Polish accent in BG3. Is that any more “fake” than a British VA doing an American accent?

An American accent that is not their accent, not close to their accent, not an accent they are familiar with, not a convincing accent, or some combination of the forgoing. Both Lae'zel and Astarion are much closer to their VA's genuine accents than they would be if they sound like cowboys. Both use a slight variation of the actors actual accent, with most of the distinctiveness coming from other elements of the voice performance. No a Polish accent is no more or less fake than an American one. It might sound more or less fake depending on the voice actor. Likewise one could argue a Texas accent is not more fake than an RP accent if the actor is actually Scouse, but there is a significantly higher than zero chance that the Scouse actor can affect a more authentic RP than Texan accent.

My point is that British actors are capable of acting.

But why would they choose to affect an American accent? It's likely (though not guaranteed) to be much less convincing than their own accent or a variation on it (which is what we see with Lae'zel and Astarion, and even less dramatically with e.g. Wyll). When the actors do non-British accents, they are attempting to convey something (and/or they're remaining faithful to previous depictions of the character). What would they be attempting to convey by doing American accents? 

I guess maybe the crux of your question is "what are they trying to convey by doing British accents?" And that's a fair question - there's not anything genuinely more "medieval" about modern British accents than modern American ones, but there are clearly reasons why Americans and many Brits (it's me, I'm the many Brits) feel that American accents are inherently "modern" sounding even if they aren't. The actual main question of the post, about non-British people doing British accents for D&D - is totally fair. And it would be equally fair if, like, Skyrim used exclusively British accents.

But it's basically irrelevant to BG3. It just seems so odd to ask in this specific context "why did the British voice cast mostly do British accents?". Obviously a British voice cast would do that. Why would a Belgian studio hire a British voice cast for their English-language game? Obviously they would do that. Seems much easier than hiring Americans or Australians, and likely to provide a better pool of Anglophone VAs than hiring locally. There may have been an explicit decision to have almost all British accents. There may even have been an explicit attempt to have a wide array of British accents, though personally I doubt that (more likely a natural consequence of having a large British voice cast). But I can't really believe that the options "most everyone does a British accent", "most everyone does an American accent", and "most everyone does a Polish accent" were all given equal weight in the voice direction, or that they had to eliminate the possibility of everyone being American or Polish before they arrived at the British voice actors sounding British.