About £1,000 with one agreed surveyor, £900 to £2,700 in the normal band, and roughly double when your neighbour appoints their own surveyor. The building owner pays, and the cheapest agreement is a neighbour who consents in writing.

Planning a side return or rear extension against a shared boundary? Budget this line item from day one; it sits outside the build cost ranges in the calculator.
A fence or garden wall on the boundary is a different question with different law: whose it is, who pays and how high it may be is on the boundary fence rules page.
When you build on or near a shared wall or boundary: side return and rear extensions against the neighbour, loft steels into the party wall, or excavation within 3 metres of their building, deeper than its foundations. You serve notice first; the agreement follows if they dissent. The document that settles it is formally called a party wall award.
The building owner, under the Party Wall etc. Act 1996: your project, your bill, including the neighbour-appointed surveyor if they choose their own.
Often: talk to your neighbour before serving notice, share the drawings, and ask them to consent in writing. Consent means no surveyors and no fees; a schedule of condition (a few hundred pounds) is still a smart voluntary extra.