Aaagh!! No!!! Not a bloody BT Homehub!!!
The problem you've described is most commonly related to the router failing to connect properly with the Domain Name System (DNS) server. That's a special computer which translates website names (such as www.google.co.uk) into their 'real' (numerical) addresses (such as 209.85.143.104). Routers are normally configured to 'automatically assign' a DNS server but, when that fails to work, it's possible to override that setting and enter the information manually. That's what I was hoping to help you do, Dot. However the BT Homehub is a SPECIAL type of router which will ONLY use the automatic settings to access BT's DNS server so, regrettably, I can't help you after all.
However I can possibly help you to check whether it really is a DNS problem. In your browser's address bar (where you'd normally type 'www.google.co.uk', or similar) type this:
209.85.143.104
Then click the 'Go' button. If the Google website appears, you've definitely got a DNS problem. (If so, get BT to replace your Homehub). If you still can't see the Google website, I'm completely mystified!
Chris