What kind of tenancy is it? Presumably an assured shorthold but for a fixed term of say 6 or 12 months?
If it is for six months they are now on a rolling monthly periodic assured tenancy which can be terminated by a section 21 notice (giving two full months notice ending on a rental date - so if you gave it tomorrow, it would end on 31st August/1st September depending what the contract says. You would then have to issue accellerated possession proceedings.
If it is a 12 month tenancy, whilst you can serve a s21, whether you can issue proceedings will depend on the terms, normally you cannot until the fix term is up but in any event you can serve a section 8 Notice on Ground 11, which is persistent and late payment of rent.
The differences between the two proceedings are that a s21 notice possession (unless you are a local authority or housing association) will normally be granted on the papers without a hearing within a fairly short space of time of the proceedings being issued (you can issue proceedings on expiry of the notice)
If you issue proceedings on a section 8 notice, on Ground 11 - the court will have to find that there was persistent late payment AND it is reasonable to make an order - it is discretionary so you would have to explain why late payment causes you problems, especially if it is received within short order and there are no actual arrears accruing. You have to wait two weeks between serving the section 8 notice and issuing proceedings, and the court will not list the hearing for at least 28 days. There is an actual hearing and you would have to go to court to argue your case.
See landlordzone.co.uk for more advice and have a look at the CPR Rule 55
I'd probably serve both a s21 notice to expire at the right time (either 31.08/01/09 or end of the tenancy if a 12 month on) AND a section 8 Notice citing Ground 11 and see what they do.
HTH