I'd be very, very wary of having work like that done. You need to know what's causing the damp and eliminate that cause AND let things dry out for a few months to see if any work is necessary.
Check all pointing, guttering, downpipes and drains for any leaks, (also plumbing of course), fix them. Make sure the current DPC is two bricks about ground level (if not, the outside levels need reducing). Ensure the house is ventilated as it should be (window vents, if none, regular opening of windows, make sure all kitchen and bathroom fans are working properly. Are any underfloor vents blocked? (if so, unblock them). Do all that sort of stuff first, and wait for 3-6 months for the house to dry out before considering any major work.
Most of the time this sort of work is unnecessary, even harmful. Please, please, have a good read of this website before committing to any 'damp-proofing' work. https://www.heritage-house.org/
We got told the same as you in similar circumstances when buying- with a quote of round 13K plus redecorating. Fortunately we are experienced and knew it was bullshit. We went the route of ventilation and dealing with such things as the above where applicable. The house dried out in about 6 months. We did no stripping of plaster and skirtings (except for other reasons in some places as it is a doer-upper!), absolutely no tanking, no injecting DPCs, no removing electrics, no mess, no bother. The costs were negligible, and most of what we did would have needed doing in any case (like new gutters and drains- this house is 100 years old and was very tired when we bought it). One thing I did ned to do- ironically- was remove some old tanking. It was making the wall wet. Once the tanking was off, the wall dried out....just as the Heritage House surveyor we got in after we bought the house predicted it would......
Had we done the work the original cowboys said was needed, we would a)not have solved the damp, and b) would have damaged the structure of the house.
So do be very careful about all this.