If the vendor lives in the same property as the tenants (e.g. in a separate flat) then it's likely that the tenants will be 'occupiers with basic protection'. In this case, if they pay their rent weekly, he can give them 4 weeks notice to quit. (It's much the same if they pay monthly. The notice period is then one calendar month).
If the landlord does not live in the property, it's likely that the tenants will be 'assured shorthold tenants', probably with a 'periodic tenancy'. In which case, unless they breach their tenancy agreement, the landlord must give them two month's notice to quit.
If no such notices are served, and title to the property is transferred to you, then you will become the landlord and have to serve similar notices yourself.
The previous paragraphs seek to simplify some rather complicated laws. The primary reference source (written from the tenant's perspective) is here:
http://england.shelter.org.uk/advice/advice-41 42.cfm
Chris