Hi,
For 4,000 euro I would expect him to put in your whole new driveway!
Can you get him to break down the costs. If he has to break the footpath to connect to the stopcock, he needs a special license and insurance etc or hires someone to do it. This could be easy be 3,000 of the costs. If so, then maybe run new pipe as far as you can in your property and then connect to the last few feet of the old pipe. If you find the pressure is still bad you could bite the bullet and get the last few feet replaced.
I think in the UK the council may pay some of the costs if the old pipe is lead. If could be worthwhile looking into the rules here.
Towger.