While there are rival claimants to the throne which some people apparently might support, none of them actually assert their claim as far as I am aware.

However, this is asking a question about modern issues - likelihood of a challenge of claims, so I have to remove it. /r/Ask_Politics might have an opinion, but I don't know if it would fit in there. /r/FutureWhatIf could also help you brainstorm the possibilities. /r/unitedkingdom seems to be the main UK subreddit, so that could also offer some insight. There is also /r/askUK.

If, however, you wanted to resubmit asking about the history of rival claimants to the throne (The Jacobites being the most prominent probably) through the past, that would certainly be allowed.