What you're looking for is more commonly called a "matted" or "mounted" print. "Card framed" seems to be a British term.
Several labs in the U.S. will sell you a matted print, and I'd imagine some in the U.K. do, too. The problem is that if you intend to sell your work, the cost of a lab-mounted print gets prohibitive. As an example, one lab here sells an 8x10" print matted to 11x14" for US$22.
Matting your own prints is easy, and a quick trip to your favorite search engine will net you dozens of tutorials on how it's done. I buy the show kits that dpollitt mentioned in his answer. That plus the mounting tape and the print runs me about US$7 for the supplies to make a mounted and bagged print, or about a third of what a lab charges. I also figure in some amount for my labor to assemble it, which still puts me well below the lab's price.