You might like to look at the website for the Totally Thames festival for events taking place on your dates.
This concert in the Bascule Chamber "under" Tower Bridge looks very interesting:
They expect it to sell out. The bascule is the large chamber housing the counterweights that assist with lifting the bridge. Some of the concert bookings include a tour of the bascule chamber.
Or if you have always wanted to try mudlarking ( which requires a permit from the Port Authority if you intend to dig) there is this: