The North Norfolk Railway. A lovely little train ride to the seaside. The railway travels between Holt and Sheringham through some beautifal countryside. It costs £11 for adults but under 3s are free. Very accessible although buggies have to be stored in the guard van. The staff are really friendly and are have happy to help you fold buggies and board the train. Toilets are situated at each station but I didn't check out the baby change facilities. Dogs welcome too.
Starting place for the Harry Potter tour! The tour takes 1-2 days to complete, but it might be good to stretch it to three to actually do some of the attractions that you pass on the way (like the Tower of London or the Globe). Best part, it's free!