Hi Owen,
Alto or tenor?
£50 probably puts you more or less in the second hand market, but that doesn't mean you can't get a good mouthpiece with that and a lot less.
I've had a bit of luck on ebay, but it's worth making a list of mouthpieces you are interested in or the specific makes, then save the searches so that you get emailed. That way you don't get tempted into something that sounds intriguing but is perhaps a little unwise.
Personally I think Vandoren are a great make and the Java and V16 range seem really good. On alto I play a Java A35 which has suited me well, I had an A45 as well but sold that.
I recently picked up a used V16 7M from ebay for £25, I was the only bidder and it's a great mouthpiece. I'd been wanting to try a 'meyer' type mouthpiece but didn't want to spend loads as the tenor is more my thing, so I worked out which makes made something meyer-esk and saved the search, a few weeks later the V16 came up and now it's here.
Thinking about it I've also got a E. Rousseau NC4 knocking around somewhere, that's another good make that doesn't seem to get mentioned much, and they also seem to sell quite cheaply on eBay, but don't come up too often.
Sorry I'm in a rambling mood,
All the best,
Chris