This is a rare example of a movie where Brits are played by North Americans and not the other way around.

Renee ZellWeger as Bridget Jones
James Marsters as Spike in Buffy
Clark Gable as Fletcher Christian in Mutiny on the Bounty
John Hillerman as Higgins in Magnum P.I.
David Healy as Dr Watson in The Sign of Four (1983)

Well, Winona and Keanu might provide a good example of why it doesn't happen more often. Reeves received most of the flak at the time, but Ryder's accent is also pretty ropey. See also: Dick van Dyke in Mary Poppins.

Here's a few. Some excellent, some indifferent, some a bit dodgy -- but none of them at Keanu's level:

Renee Zellweger - Bridget Jones
Emma Stone - Poor Things and The Favourite
Gillian Anderson in a number of things (but she grew up in England and her English accent is actually her own)
Johnny Depp - Captain Jack Sparrow -- and he seems to affect a vaguely British accent in various other roles too for reasons best known to himself
James Marsters and Juliet Landau -- Buffy the Vampire Slayer
Maggie Gyllenhaal - The Honourable Woman
Meryl Streep - The Iron Lady
The entire main cast of This is Spinal Tap
Gwyneth Paltrow - Emma
Natalie Portman -- Star Wars and -- if memory serves -- V for Vendetta
Chloe Grace Moretz - Hugo
Robert Downey Jr - Sherlock Holmes
Kristen Stewart -- Princess Diana in Spencer
John Lithgow - The Crown as Winston Churchill

On the whole Americans are pretty weak at adopting a convincing English accent. The only flawless one I’ve seen is Paltrow in Sliding Doors.

No one mentioned Dick Van Dyke in Mary Poppins or Kevin Costner in Prince Of Thieves😂

Mel Gibson - Fletcher Christian, William Wallace

Robin Wright - The Princess Bride
Lindsey Lohan - The Parent Trap remake
Michael C. Hall - Safe (British mini-series).

Generally over the last 15 years or so, I'd say it's become much easier for American actors to do a British accent because they can just check out a film or TV show now to study with the click of a button on their phone, and even look into different regional accents. Whereas before, a lot of Americans probably thought we all either spoke like royalty or cockney. In the same way, a lot of us used think of the American accent as either Californian, New York or Texan because 90% of Hollywood films seem to be set in NY and LA, and the dumb southerner stereotype occasionally appears in one.

Some nice examples here. Mel Gibson spent most of his youth in Australia, though, so he would have an easier time imitating the accent. Is the Jack Sparrow character meant to be British? Didn't know that. RDJ as Sherlock I forgot obviously. Spinal Tap is meant to be a British band? Didn't know that, have only watched clips from it.

John Lithgow played Winston Churchill in The Crown.

Gillian Anderson played Margaret Thatcher in The Crown.