Tate Britain

While the Tate is buggy friendly and a nice place to take a toddler, you have to keep your hands on them at all times.  Many paintings have small ropes and posts beneath them, at about shin height to an adult and easily tripped over.  Small children are drawn to these and make the galleries at the Tate unsuitable for an adult with two toddlers in tow.

 That being said, it is a lovely time to take a small child to the Tate and admire the Pre-Raphaelites and the Beaux Arts building.   

 The cafeteria is slightly challenging on your own with a small child and the tray, but the space is buggy and child friendly if it is not too crowded.

 Outside, the gardens at the Tate are a wonderful place to spend time with a toddler.  It is not enclosed, so you do have to keep an eye on them as they can easily wander towards Millbank Road.  There are different sized pebbles and rocks that are incredibly amusing for small hands.  Over by the Milbank entrance, there is a small pond to play near or fall into, depending on your energy level.