If the tenant is occupying under a tenancy agreement then you can evict on the basis of rent arrears inu the following circumstances under s8 ground 11 of the housing act 1988:-
Arrears must exceed 8 weeks if the rent is paid weekly or fortnightly, 2 months if paid monthly, one full quarter if paid quarterly or 3 months if paid yearly. The maximum arrears in each case must exist both at the notice of proceedings and at the hearing itself.
If your tenant required compensation then he should have formalised the matter and provided a detailed breakdown of their loss, rather then let arrears accrue and then retrospectively/vaguely claim it was for compensation. The judge won't like that but it will be up to him as to the credibility of your respective positions. They will also not like any time lag between when the loss for which compensation is claimed and the date when rent arrears started accruing.
The standard of repair your a obligated to maintain is here::-
You are probably going to have to fight it out in front of the judge with them. If the fixed term of the original tenancy agreement has expired then you can issue a s21 notice for possession giving two months notice as the tenancy is now a statutory periodic tenancy (ie. one which rolls over from one rent period to the next). You do not need a reason to issue this notice so you may consider using this as a fall back option to getting them out.
NOtices should be in the correct form and you can obtain them fromi any online document provider.
Hope this clarifies, if so please kindly click accept.