This dates back to pre Housing Act law. For hundreds of years back into the past, landlords have been able to evict tenants under a rule known as ‘forfeiture’. Under this rule, if the tenant breached any of the terms of the tenancy agreement then the landlord could ‘re-enter’ and end the tenancy.
In the distant past the landlord would end (or forfeit) the tenancy by physically re-entering the property (and I understand this can still be done in some circumstances for commercial premises). However since the Protection from Eviction Act 1977, residential tenants are protected from this. The act provides that it will be a criminal offence (and also entitle the tenant to claim compensation) if the landlord repossesses the property other than via the court bailiffs, after obtaining a court order for possession.
Forfeiture was perhaps most frequently used for non payment of rent. However a landlord could also forfeit for other breaches of the tenancy agreement. It is in these circumstances that landlords had to be careful not to accept any rent, as this would mean that they had accepted the breach. As by doing this they would confirm the tenancy and no longer be able to proceed with the forfeiture claim.
Forfeiture and the old rules relating to it seem to have sunk deep into the collective memory of landlords. However their fears are (largely) groundless.
Forfeiture was done away with in the Housing Act 1988, and cannot now be used for assured or assured shorthold tenancies. Indeed in these cases, if a tenant offers rent and it is refused, the tenant will then have a defence (for claims for possession based on rent arrears) as they will be able to say that the landlord has failed to mitigate his losses by accepting rent which was proffered to him.
Where possession is claimed under section 21, whether or not the rent is paid is wholly irrelevant (to the court claim that is), as s21 claims are not connected to rent, the right to possession arises after the section 21 notice has been served and the notice period has expired. Paying the rent is not going to affect this.
Forfeiture is still relevant for protected tenancies under the Rent Act 1977, and for common law tenancies, i.e. those which do not come within the scope of the Housing Act 1988. Common law tenancies mostly occur where the rent is over £25,000, where there is a resident landlord, or where the tenant is a limited company. However if you are forfeiting for non payment of rent, the tenant always has the right to ‘relief from forfeiture’ if he pays up, so refusing to accept rent is not going to do you any favours.
Technically it is possible to forfeit, for these tenancy types, for other breaches of the tenancy agreement. However you have to serve a special notice first and I have never known any actual cases, at least for residential short tenancies. If you have any experience of any, I would be interested to hear about them.
So far as I am aware though, this would be the only time a landlord would have to be careful about accepting any rent (and should not do so before speaking to his lawyer).
But apart from this, very rare situation, you should be safe to accept the rent. And consider yourself lucky – very few tenants pay up when they are being evicted.