The ACTUAL reason why there are so many British actors in Hollywood movies is because of the financial credit that UK government provides.
Now, try to remember a British actor in an American movie. There is a 90% chance that movie is a blockbuster or what I mean by a blockbuster is high budget/production movie.
In order to improve and attract the local movie productions/studios, UK government offers a financial credit to the studios. And studios being studios take as much as advantage from this incentive. And in order for a movie or production house to qualify for this incentive credit from UK government the movie should check couple of boxes:
1. Major part of the production should be shot in UK
2. Certain % of leads/actors should be British
3. 862
The production should be of certain budget
And a few more which I don't remember.
So as the Incentives are a good eye candy for the studios, they do there best to take the gist of it.
The reason why most high production movies have lot more British actors is they qualify for the 3rd point above and they have necessary budget to shift there American crew to UK and start the production. You can see any low or medium production movie probably less than $100 mill and mostly they have only American actors cause they may not qualify for the 3rd point above and even if they do it is not feasible to move the US team to UK as it eats the budget.
The best example I can give you is of Blumhouse production movies which is based in US and they make low to medium budget horror movies and look at the cast and mostly it is 100% American. And why don't the Blumhouse movies have British actors? cause it is not really feasible to them to move the production outside and also they won't qualify with there low budget for the incentive.
And it's not just the UK, many countries also provides these incentives. Norway, New Zealand, Australia and Canada. You'd be suprized on how many hollywood movies get shot in New Zealand.
The reason for these governments to offers these incentives is coz movie jobs are highly paid and by having the production in there country it will employee thousands, improve technology and kinda free tourism marketing for the country.
So by giving these incentives to the studios, indirectly this will employ thousands and return huge in tax for the government. So it's a win-win for studios and the Country.
Sources: Highly recommend to watch this
Film tax relief 824