Long Term Double Room with Garden House

Hello,
I am a British citizen living in North London. I am looking for a double room in a house with a garden, preferably on the ground floor or first floor.
I have one well-behaved domestic cat. The cat mostly stays in the garden, walks around during the day, and sleeps in my room at night. It does not cause any damage and does not stay inside the house.
I am currently living in a single room, but it is too small, so I am looking to move to a double room. I have been living in my current house for 5 years, I am a long-term tenant, and I do not smoke.
Preferred areas: Edmonton, Turnpike Lane, Wood Green, Finsbury Park, Seven Sisters.
I am looking for a pet-friendly, animal-loving household where the cat is not a problem.
Thank you.