I have donated childrens books to Guys Hospital which has been very pleased to have them. I took them to the minor injuries after having used the facilities there and noticed they did not have anything for kids to read. I think they have also taken them upto the childrens ward. I guess they might well welcome toys too. Also consider giving them to your local doctors surgery or local nursery.
As far as the toys and clothes are concerned you could always offer them on Freecycle - often organisations post 'wanted' as they are looking for such items - it's a fantastic way of finding new free homes for stuff you no longer want ... or have room for!
Southwark Tourist Information Centre is holding some charity events this Thursday 28 July including a mini fete and a party. (As featured in this week's SE1 email. One of the causes is for educational projects in Sri Lanka and they did request that people drop off any children's books for them to send to the projects - so if you have any spare that would be great.
The fete is happening from 10-6pm but there is also a free party in the evening from 6-9pm so you can drop them off then if you can't make it during the day, and enjoy the party at the same time!