Yeah, the idea of Biden as being part of the Tory Party is absurd. People from Biden's background don't easily become Tories. He'd be on the right fringes of Labour, but Labour nonetheless.
(He sure as hell wouldn't be a Lib Dem or a CUK, if anyone wanted to suggest that. Biden is a big party man who wants power. He'd never join a minor no-chance outfit)
He's also an ethical man who wouldn't bow and scrape before the current Strasserist leadership of UK Labour, but that's an unusual situation. Biden would clearly be in whatever the center-left party is in any modern country.