Hi,
Right this can be a big can of worms if you aren't careful. First off you need to make sure you have a secure admin password, or else your router settings can be accessed.
Also you could be liable for anything done on the connection, and there's no way of you being able to prove otherwise, as all usage is tracked through your broadband connection username. Now that's not to say your neighbour would do anything malicious or dubious, but you have to be aware of it.
Internet providers don't have huge racks of servers for nothing you know.
Now there is one option they could consider that would keep you in the clear - BT Openzone. If you have a Business Hub then they could buy some minutes, or if they're a BT Business customer they may have free minutes.
Then they could log in to the Openzone signal from your router (assuming it's active), and do whatever they like without affecting you (other than nicking a bit of your bandwidth).
Hope that helps.
Cheers.
Dave A