1.Possession order alone
or 2.possession and rent arrears
The rules change a lot but they used to treat 1 much more quickly than 2.....
https://www.gov.uk/evicting-tenants/accelerated-possession-orders
It then depends on whether they have delivered the summons - tenants in arrears really do --- not answer the doorbell
and they wait fourteen days
and either grant it or.... if there is a defence set a court date. In the interests of Justice the tenant will be heard in court whether or not he has broken all the rules
get the order
then wait a time for them to get out and a Bailiffs order
So it is in months
Now..... you should have got a guarantor - Used not to, but it is absolutely essential if you are going to re-let to another tenant. Then you say, get them out by the week end and I wont go after you for the rent. quicko quicko, greased lightning
OR
go to them and say
"People who dont pay the rent dont have the rent
if you get out, I agree not to sue for the rent. This is an enforceable contract"
which it is because they are providing a service ( getting out) and you are giving value ( agreeing not to sue)
good luck