I'd definitely recommend Bill's restaurant in Victoria. bills-website.co.uk/restaurants/london-victoria/#menu
The Science Museum is probably the best for toddlers.
The Pattern Pod is located at the very rear of the museum, on the ground floor and offers a wonderful experience for small children. The exhibit is officially designated as being for 5 – 8 year olds, but there are many interesting, hands-on things for your toddler to investigate including dress up clothes for children to try on and play around in. There are tiles that children can insert into a special display that projects different patterns on the ceiling, pattern puzzles and a pattern making art program plus much more.
The Garden is a real treat to take your children to, its well-hidden in the basement so ask about it if you do not find it on your own. The first thing you notice when you walk in are small children wearing orange protective aprons playing in the most elaborate water table you have every seen. Filled with small boats that float down a cascading canal, children are able to work different levers and pumps to direct the water and boats. It is really great fun.
Further along is a play area that suggests a building site, with giant blocks you move around a small climbing frame using wheelbarrows, bag and pulley rope, a chute or any other imaginative ways toddlers can derive.
There is an area of soft toys, an amazing multi-sensory room, puppets… I know I am missing some things, but you will have to see for your self.
The picnic areas are right outside The Garden, basically a large area of steps to eat on, or you can go to any of the cafes or restaurants.
The Transport Museum is Mecca for all children. Spread over three floors, the museum has different models of the various means of transport through the ages for children to climb into and explore. Especially on a rainy day, it is well-worth the admission cost. There are two designated children’s play areas, one with dress up with a model bus to drive and the other is for even younger children with life-size model wooden boat, bus, taxi and tube car to play on in addition to a large model city with trains and buses to push along.
The Kids Zone at the National Army Museum is one of the best indoor play spaces in London AND its free. The only drawback, the entry is limited to 30 children, so there is a slight gamble that you could show up for the timed entry and it is filled and you have to wait for someone in the session to leave early from it. The Kids Zone has two enormous soft climbing frames with tunnels, slides, netting, rolled cushions, but much of it hidden, so an adult needs to accompany if your LO is not very steady yet. The Kid’s Zone also has dress up, a play kitchen, trains, cars and books.
As a bonus, outside the museum are picnic tables for you to bring your own lunch and eat outdoors.You are just a few blocks from Duke of York Square and the Kings Road, so you can easily mix a shopping trip in as well.