I had this, it was an old house and the 105-year-old lead pipe had burst somewhere underground. Couldn't find it to the front of the house (dug a hole), couldn't find in it a guessed place under the sideway (made a hole in the concrete) so put in a new plastic water pipe and discontinued the old.
It was not unbearably difficult, as the front was gravel so not too hard to trench, and the new pipe was laid under the suspended timber floor in the front room, the kitchen was behind it so the new pipe came up in the corner.
I took the opportunity to lay a larger plastic pipe, which gives much better flow, all the way to the stopcock just inside the boundary (the meter was in the adjacent pavement). I hired a labourer to help with the heavy work (digging holes is hard work). The new plastic pipe (get 25mm or bigger) is quite cheap, and is flexible so easy to lay. You should not need any joins between the pavement and the kitchen as it is available in 25metre rolls from any builders or plumbers merchant. You will need new stopcocks to fit. If you have a combi or megaflo, run new larger internal pipes as well to get the full benefit.
Thames Water have a scheme where they contribute to the cost of replacing a leaking service pipe. They also have a lead pipe replacement subsidy, but they have to take a sample of drinking water at the kitchen tap to see what the lead content is, and they were so slow in coming that I had replaced the pipe before they came. If you have lead pipes, ask immediately for a sample to be done, perhaps you will qualify for a subsidy. Some water co's will replace any of their own lead pipes if you do your bit. this makes it very much easier and cheaper to connect your new pipe to their new pipe. TW gave me a rebate on the wasted water once I had replaced the pipe.
If you dig the trench yourself, it will be cheaper than paying someone else. Many plumbers don't like heavy work. The water co will inspect your trench and pipe before connecting, unless you pay one of their approved contractors. This is to make sure it is at the required depth (from memory, I think 450mm). They will charge you a lot if they have to dig a hole to connect your new pipe, unless they are doing work themselves, for example replacing lead pipes they own.
If it is difficult to dig a trench, you can hire a company who will use a mole machine to bore a little tunnel for the pipe. It will not be cheap.