GOT had a fine list of British actors in its cast, but, no, there are plenty of British actors that haven't been used for the show yet. Most are likely too big to be on the show, like Fassbender, Cumberbatch, Tom Hardy, James McAvoy, and Martin Freeman. All those names have far more presence and acting skill than the likes of Richard Madden, Kit Harrington, and Sophie Turner, lol
There's also Judi Dench, Helen Mirren, Daniel Craig, Ralph Fiennes (and anyone else from HP which hasn't been on GoT), etc....But I doubt HBO would be able to cast any of them, either.
A British actor they could cast is Richard Armitage. Same with Cillian Murphy. I'm sure there are others I could come up with. Hell, since that madman Zaslav canceled Raised By Wolves, some of the British cast on that show would be fine additions. Niamh Algar, Abubakar Salim, Cosmo Jarvis, and even Travis Fimmel.