OP here- Thanks for the suggestions! Yes, DH will be coming along.

Will you have another adult with you?

Agree that you should go for you and check out London as an adult and have fun!

At that age, go for you. See what you want to see. Your child will be as fascinated with a squirrel in the park as they are with the Changing of the Guard. Our kids were perfectly happy in a neighborhood playground in a public park as they were some fancy place (where you had to pay).

The Science Museum (South Kensington) has lots of hands-on play - buttons to push, water to splash.
The Diana Memorial Garden in Kensington Gardens is pretty cool - a giant pirate ship for clambering.
Open-top London buses.
London Eye, South Bank, is next to the Aquarium.
Regents Park zoo.
Legoland is at Windsor but would be worth a trip. It's a toddler's paradise. If the weather is good, bring your toddler's swimsuit as there is a fountain play area for them to splash around in.

I am traveling to London in August for a conference and am considering taking my DC who will be 16 months when I go. The conference is for a week, but I'll like extend the trip for a few days on both ends. For those who have spent time in London with a toddler in the summer months, any advice on things to do, places to go?