That sounds great I have no specific advice (other than to suggest a river trip maybe) but was going to say keeping it general and flitting from one thing to another is good.
I love the museums and galleries and was keen for dc to go but if you only have a day, we've made the mistake before of building up the exciting trip to London then spending the whole day in one museum. Dc didn't get much of a feeling that they'd 'gone to London' iyswim.
(Btw M&S Angel bras are perfect first bras for girls)
Gilly Hicks have a lovely syst where you try on a selection of bras. They're expensive though, and its a Hollister like grotto experience. Wear comfy shoes. It's a glorious day and you'll Want to be out as much as possible. Carnaby street/ liberty is a lovely enclave. National History/ Science and V&A are close to each other- British Museum is a bit out of the way from other activities and a bit 'big'. Where are you coming in to?