I am house owner and when I bought my 3 bedroom house I decided to give Two rooms on rent. Box room and bedroom. I have people living in other rooms and I live in the master bedroom. My issue is that When I rent the room I didn't get my tenants to sign any paperwork. (Tenant agreement form).

I gave them 1 month notice to empty the room they said OK but when the time was up they Said we need more time as it was hard to find another room.

I decided to give them 3 more months, from December to April. Now time is almost up and they are refusing to leave. What actions can I take against them?

They always pay rent late and leave everything dirty in kitchen and bath, etc but of course I don't have proof of that.

Am in UK by the way.

Go to your local housing authority and find out the rules for evictions. You should have never rented rooms without researching what being a landlord means. They are taking advantage of you and you are letting them.