The tenant would need to be at least 2 full months in arrears before you could take action to remove them - I believe this is the Section 8 route. You should be able to find links to these and other forms here
http://www.landlordhelp.co.uk/
Depending on the tenant, a letter may shake them up, but in reality it would have no effect and you would need a Court Order to evict them from the property.
Unfortunately it's not very easy to evict a difficult or non paying tenant.
One piece of advice would be, in future, to only issue a 6 month AST and then let the tenancy go periodical after that for which you would only have to give 2 months notice using a S21 form (this would still have to go to Court with a non complying tenant but it's mandatory for the Judge to order the tenant to vacate with this method)
In your present situation you may be lucky and the tenant quits or pays up after you issue the Section 8 notice.