Unlikely you will find one person to do a complete bathroom. I know of several plumbers who think they know about electrics. I know electricians who think they know about plumbing. I know builders who can do everything - or not.
You could try a local jobbing builder who will pull the required trades together. It depends if it's a refit or additional as you may need, carpentry, tiling, electrical, plumbing, heating, plastering and brickwork skills.
I know someone who'll do the trick, and if there are any parts he can't do, he has contacts that'll come in and do those parts.
He did a brilliant job on our bathroom a few months back, and was clean, polite and helpful. Would use him again for anything in the future.
He does bathrooms, kitchens, pretty much anything really.
http://tinyurl.com/3tr28xo
If its anything like ours you will probably need a plumber, electrician, plasterer, tiler, painter and maybe even a brickie if you end up with external holes to fill..
If you contact Nigel at Associated Plumbing in Berko- he is part of a team who are used to working together to do bathrooms and kitchens - anyone of them will project manage and organise the others to come in and do what is neeed - but will give you a price for the whole job Great guys all of them.
I've used Nigel Earle (Associated Plumbing Services) for gas cooker installation and flushing out our CH system, and can vouch for his work. He must be good, because it's often difficult to get hold of him. He tends to do larger jobs, so maybe not ideal for a bathroom. Worth trying tho'. We used a guy called Dick from Hemel Hempstead (01442 242489) for refurbing our bathroom. He did a good job and co-ordinated with his colleague who did the tiling. We didn't have significant electrical works done - if you are, you'd need to involve an electrician who is certified to do Part P (Building Regs) electrical installation work
Now you are safely moved in a part of the Berkhamsted community - see what is going on http://tinyurl.com/3p3x9ra
£120 - £135 pa
£350 - £450 p day
£350 - £400 p day