Couple break up rent arears

Rent Arrears

Hi
I have a property in Chesterfield, the couple we had in were no trouble at all for months 'until they split up' now I have the guy living there on his own the last 2 months, last month he paid his rent 2 weeks late and this month nothing at all yet.
my questions are,
1. does his refusal to go through re referencing with the letting agency to sign a single tenancy give us the right to evict.
2. although not fair on the girl can the letting agent approach her for the missed payments as she is named on the joint tenancy.
3. finally if there is no tenancy agreement in place as such at the moment as the girl has left can we serve anything without going to court?
Thanks.
Glyn.