UCITS and AIFMD (depending on the type of fund) have a passporting framework to allow funds from one place to be sold in another when they meet certain standards of compliance in a ruleset that all the European regulators have said they're happy with.

Given the importance of the financial sector to the UK, the government will not be keen to unravel the agreements and standards that facilitate cross-border investing.

Even if they did put some silly restrictions in place as part of the overall negotiated package (i.e., you won't let our funds seek investment from your investors without now jumping through loads of new European regulatory hoops, so you're not allowed to continue soliciting ours without addressing all these wildly different UK regulatory hoops) it seems pretty unlikely that a fund which can be sold to the public in Germany and Netherlands and Luxembourg and Ireland would not, relatively easily meet the standards to be made available in UK. Especially on day one, before we have chance to create any stupid new regulatory protectionist hoops.

Potentially, worst case scenario they would cancel their London listing, with some notice period, and you would have to use a different stock exchange instead. Or maybe the act of doing that would cause the fund to need to shut down because of being too reliant on the support of UK investors who started to find it too difficult to bother investing, and you would need to sell up.

FWIW I have holdings in some London listed funds or companies which are domiciled in places like Guernsey or Jersey or Bermuda, none of which are in the European Union.