Sadly, that $4K isn't going to go a real long way in UK...it's a pretty expensive place. You'll need to find seriously cheap lodging and really mind your pence!
If you're not really stuck on UK, you might look at other places where English will do, including Jamaica and Puerto Rico or even Guyana.
If UK is really IT, though, you should look into hostel costs, and into sharing sites like couchsurfing.com. Depending on when you're going, you might find some luck with college spaces that are out for the term, and things like that. If you can keep your lodging to average $40 a night, you'd have $2800 left for the rest, or about $90 a day. Sandwiches and supermarket takeaway can help stretch it.