Ebay UK is a good resource for you, as many UK sellers won't ship, and that tends to keep the prices fairly low (although the fixie craze seems to have bumped prices up in the last year or two). If you do a search for bikes within driving distance of Manchester, you'll be able to find something decent for under $200. Focus on quality tubing and components, rather than brand name. Either an 80s Japanese bike or a small brand English bike from the 70s/80s would be a good choice .

There a LOT of great local Engish builders, and while some of their names won't fetch as much money as more well known brands, you'll have yourself a great bike.

The most important criteria is proper fit. Do a search and you'll find plenty of information. The downside of buying on Ebay is that you generally can't test ride, but if the seller is near by, you could always ask.

Best of luck!