You have to look at both sides:
1. Vendor - how quickly can they move out, are the deeds available, is there sufficient money to pay off the mortgage.
2. Purchasers - how long will it take them to organise their finances, do they need to sell somewhere or give notice in rented accomodation, have they the funds to close.
Realistically, 4- 6 weeks from agreeing the sale is the norm. It can be done in less than a week if everything is sorted. But that is highly unlikely.
mf