as long as the lead pipe is still there, they will carry out a lead test and unless very low, will have to replace their bit, and may give a subsidy to help you replace your bit. It will anyway be far easier to connect your bit to their new pipe, and you might be able to persuade the fitters to do it if your trench and new pipe are ready when they come.
Also, see if they have a program or subsidy to replace leaking supply pipes.
Maybe yours has a leak in it.
I recently had to replace a leaking lead pipe, but they did not test the water for lead until after I had finished, due to long appointmenting process. They would have charged me £500 to connect my new pipe to their meter, so I just joined it onto the stub coming through the boundary. Luckily their meter had a stop cock on it under the pavement.
p.s. there was a report on this in "Which" recently. The different water companies vary a lot. Thames Water is one of the worst.