I used a guy called John Smithers who is a local plumber. He was excellent and I couldn't recommend him highly enough. Fixed a leak for me that had caused damage. Came out twice, once to fix the leak and the other to make good the tiling etc and for all that he charged me £170 which I thought was really good considering a call out plumber charges £100 before even looking at the problem!
You could probably plumb the dishwasher in yourself, I understand it's very similar to plumbing in a washing machine. I haven't done it myself (I'm not allowed to order another dishwasher after ordering one which was the wrong size, Mr Zoe was most upset), but I found plumbing in the washing machine very easy, and I'm pretty useless.
If you go to the hardware store on Lower Marsh, they will find what you need and give instructions. I recently took in the inner bit of a tap that must have been leaking for two or three years (I know, it's terible, I just couldn't get around to doing anything about it), and they found what I wanted, and didn't laugh when I asked if it was the right piece, as it looked so different. They patiently explained that the extra bit on the tap was the washer, which had completely gone on my tap...it explained why it had been spurting hot water everyhere.