I've just asked Chat GPT for you. It said mid-range fence panels 6' tall are £40-£55 each. Noted that concrete posts are being reused - but there may be some extras (eg screws, gravel boards). Based on £50 per panel = £1200-£1300 for 20 fence panels of 6' tall each..
Then there's the labour costs. They say most fencers will charge a day rate - of £200-£400 each.
There's a variety of other "bits and bobs" - eg if you want them to dispose of the old panels etc for you there will be a charge.
Don't know how long the fence is - but it sorta confirmed my feeling that £2,000 is probably not an unreasonable charge.
It's a blessing that you can do this with a fence - as I had a great long tatty unmatching fence with no concrete posts on the house here when I bought it. Well I did have - until the first winters winds - they're strong and frequent here. Don't even ask what the cost of the wall I replaced it with was......it comes in "eek" territory, especially as I'm from an area where walls are usually brick and not concrete blocks (so yep it had to be brick - to match my West Country tastes). It's probably part of why my hair turned white at about that time.....
So that price really doesn't sound too bad to me - unless it's only a couple of panels long. Better still if the neighbour will pay 50% - and yep...it's worth checking whose responsibility it is - in case you get lucky and it's a joint thing.
Another assassination attempt on Donald Trump
The main room in your house...



