Widow friend of mine with rat infestation in her detached Victorian house had professional advice that they "probably" entered through drain. A "Drain" company came and put in a camera
(15 minutes £240) and reported later - with photographs - her drain had suffered subsidence showing evidence of clutter like pebbles, bits and pieces - £2850 + VAT to clear it!
Does all this sound appropriate? Not happy to give the go-ahead without asking for advice.
Impossible to say,without seeing it and haveing knowledge of such things. Ask for more estimates from other companies.But as you say there is subsidence it will NOT be cheap. But definitely get a second opinion and estimate.
Are they just going to clean it out, or replace the drains completely? If the latter they will need a mini digger and it could be a big job. It still seems like an awful lot of money and I would advise getting at least a second quote. You are not under any obligation to use the drain company that provided the initial inspection.
I imagine the company will have to dig up the ground and replace any gravel, etc. to remedy the subsidence and/or fit new pipework to replace any damaged bits.
A general builder ought to be able to do similar and shouldn't charge anywhere near that (although my answer assumes that it is a straightforward procedure not involving costs of access, etc.).
Don't forget that in England and Wales since October 2011, shared lateral drains and private sewers became the responsibility of the regulated sewerage companies NOT the individual property owners.
Let's hope that her drains are part of a shared system.