DipTrace is what I use. The Freeware version can do 300 pins, which is more than you'll need for most small projects, and far more than you'd need for this. It's also pretty easy to get the hang of it. http://www.diptrace.com/download.php
As far as cheap boards in the UK, no idea. That's also a bit of the 2 up 1 down kind of deal also, Quantity, Size and Cost. If you only want a few small boards made up, it's not going to be cheap.
You can try BatchPCB to have one made up also, though the time frame there is what bites. There it will cost you a little more, and take around a month before you get the board, but it would have the Solder Mask and Silk Screen on it, whereas some other cheap places that will do a few boards for cheap those features don't come with that done.http://batchpcb.com/index.php/Home
The ones from SeeedStudio are right cheap, but you don't really need 10 or more of them made up for this project, but a spare or two is always good to have. They also have the Mask and SS layers on their boards. http://www.seeedstudio.com/depot/fusion-pc...h=185&r_q=q
I've used both of these fab houses before and the boards have been great. While SeeedStudio is cheaper and their turn around time is a little faster, they don't route the boards for you and you're locked into the sizes they offer, which is fine here since the smallest they offer is 5cm x 5cm and that's more than enough room for what you're doing. Anything that's not a square or rectangle I'd get done at Batch as you can make the board shape just about whatever you want. I had my 36X protos made there. Seeed also does their runs in batches of 10 and you can select from a few different thickness levels of board (Batch you only get 1.6mm) so you'll get 10 boards for that price. Either place will work fine and each has their plus/minus about them, just depends on what you're after more, a handful of cheap boards, or a few routed up in some design that fits the install better than a box shaped board.
I'd recommend Seeed in this case, as the 5x5cm board is large enough you could try a couple designs on that board size, and you have plenty of room in the Wheel there for whatever board shape. You could also use the extra space and make up or try out some other thing also. They're easy enough to cut apart with a Dremel or small table saw with a diamond blade, just mind the dust in either case.