it's not at all difficult, unless you have a concrete drive or a concrete ground floor. Wooden floors can easily be lifted to lay the new pipe beneath. Blue pipe is flexible. Pipe above ground must be insulated with "Regulations" grade foam lagging.
The new pipe does not have to follow the same route as the old one.
If it is lead you might get a replacement subsidy, or they might at least connect the new one free. Local policies differ.
Start by asking the water co to test your drinking water for lead content (this is free). It must be done before you start work.
Since digging the trench costs the same whatever size of pipe you use, I would always upgrade the pipe to 32mm blue plastic (25mm would often be enough but the cost difference is trivial). Larger pipe will give you better flow for stronger showers, and will enable you to get the best out of your combi boiler or unvented cylinder, now or when you get a new one.
Large bore stopcocks and service valves are more expensive than 15mm ones, so insist that full-bore ones are used to get the best flow, and watch that the plumber doesn't forget to fit the large ones you have paid for. It is a hundred times more work to dig up the pipe and fit a bigger valve after the job is finished.
The water co will have a list of accredited plumbers, but anybody can do it, but the new pipe will be inspected before you fill in the trench. You will have to get them to do the final connection if the public pavement has to be dug up, but anyone can dig the trench in your garden.
If you possibly can, replace the pipe all the way from the stopcock or watermeter under the pavement, to the indoor stopcock under the kitchen sink, and also enlarge the indoor pipework to 22mm or bigger up to the point where it tees off for the boiler or cylinder, or loft tank, and the cold supply. This will usually cure those annoying cold or hot moments when you are in the shower and someone turns a tap on or flushes a WC.
Plumbers are weedy little fellows with petal soft hands so the trench will often be dug by the householder or a builders labourer. This is also cheaper.