This didn't matter, as I'd factored on getting the 18:52 train from there to Hampton Court, due to arrive at its final destination at 19:14 (which is what Journey Planner still tells me, insultingly enough).
I actually got to Hampton Court at 19:43 for a 29-minute delay and £72.50. But this journey itself was exciting. And by 'exciting', I mean infuriating. After a good 15 minutes or so waiting on the platform at Wimbledon, TfL finally deemed it worth announcing that there weren't going to be any trains to Hampton Court for the foreseeable future, and that I should board the next train to Guildford, changing at Surbiton. No explanation was offered for this turn of events.