Are you asking this from the POV of a landlord wanting vacant possession,or one of the housesharers wanting out?
(Or indeed all the housesharers wanting to leave at the same time)
How long have the housemates lived in the house?
If you are a tenant with a Part 4 tenancy (basically no new tenancy agreement has been signed during the last 12 months) then the tenant should give 56 days notice in writing to the landlord. A landlord would have to give you 112 days notice in writing.
It can be very difficult to synchronise a moving out date with a moving in date because when you find a suitable property you usually can move in almost immediately and you don't want to be paying rent for two properties at the same time. Very often a landlord will accept a shorter notice period if you ask him/her.