Hellobee Boards

We have used storage ottomans with great success as both a replacement for the coffee table and toy stashing. Then we would keep books out in a more accessible basket of some kind.

This won't help you since I'm sure you don't have Homegoods in the UK, but I bought us a bunch of large natural/wicker baskets and put two in the living room and one in future LO's room - just to hold toys. They are almost empty now since LO isn't here yet and we've only received a few toys as gifts, but they can really hold a lot and cleanup will be easy since you can just throw everything in. They don't have lids, but they're big baskets and they are also stylish so that doesnt' bother me. They were only about $40 each!

@Modern Daisy: this is exactly what we did. We have a low (maybe hip height) long bookshelf with different compartments, and LO's toys are in some of them in baskets, so you can't see the toys and it looks neat. In the other compartments are books that I don't mind him pulling out.

We actually use our play kitchen as a toy box right now. End of the day I pile all of her junk into it and we just have the one cute (Kidcraft espresso) kitchen in the corner of our living space.

Do you have Ikea? The Stuva system comes in white.
There's a bunch of other pieces including ones without knobs.