Then for sure, with that list, you want to get one of the jump-on-jump-off tour bus services. I think they go to every place you've mentioned, or close enough you can walk (eg Sherlock Holmes souvenir shop is approx 5 mins walk from Madame Tussauds). The walk-up cost is GBP 20 for an adult, I'm sure there will be discount coupons to be found in the tourist brochures. They also offer a river boat cruise as a no-cost option for part of the trip.

Regards

Mark