Sussex ok? (check the CTT website as there's also one on the same course the week before)
Course here
There aren't that many 2-up TTTs during the season, should be easy enough to check all those in the London South region. Some club events may not be listed, check the websites of local clubs to see what they are doing.
Also: if a local club organizes an evening 10 (or a Sunday 25) then a word with the club/ racing sec. is often enough if you want to try a 2-up, certainly it's no problem at my club and riders who want some experience/ practice with a new partner etc. will do this in advance of an event.
I have sort of assumed you (or your teammate) can drive to the start, however I almost always ride to events. It takes a while to find out what is on in any given region- but events often have a long history and there are club members who know this stuff usually- although you may have to listen to a lot of cyclist tall tales to get to the information you want. Best place to start is the bearded club member who owns a trike.