This is almost certainly one of those 'How long is a piece of string' questions. If both the donor and the recipient of the gift have all their bank statements ready, together with their proofs of ID, such a their passports and utility bills, there's no real reason why the whole process can't be completed very quickly indeed. See here for the process
https://www.clapham-collinge.co.uk/news/a-gifted-deposit-how-to-enjoy-it-without-burdening-the-conveyancing-process
However solicitors are notorious for taking ages to complete even the simplest of tasks, so there can be no guarantee that your solicitor will be efficient.
Further it might depend upon how the donor came by the money in the first place. If the solicitor can see (by looking at bank statements) that it all came from salary payments from, say, a local authority (and, if necessary, the donor can provide proof of his/her employment with that authority), then things should be able to progress quite smoothly. However if the bank statements seem to show that the donor received irregular large payments from an unknown source, the solicitor will have to make further enquiries to determine that they came from a 'legitimate' source.