I'd resigned myself to flowers (which are really not much like balloons at all), and so went around to the south side of South Kensington station, where the nice flower stand is. There, in front of me, on the south side of the street, was a much, much larger flower shop, La Jolie Fleur, which had opened just in time* for me to go in and ask if they did balloons. None were obvious, but they did! They do! So if you need balloons in the South Kensington area, now you know where you can go too.
The store wasn't there the last time I was in the area, which was several months ago, and the staff all seemed fairly new to the enterprise.
P.S. Picocon itself was my favorite edition of the con yet. Two good short stories readings from Michael Marshall Smith and Pat Cadigan; Robert Rankin being silly and playing the ukelele poorly-by-intent (and being impatient with how long the sessions) were; a largely-topical discussion on ray guns from the three guests of honor (the sort of panel where, by design, staying on topic is entirely optional); and thus usually silliness and fundraising with liquid nitrogen and bad writing, and visits with friends I don't see nearly often enough. Also, it didn't rain.