The only pub matching the requirement is the Good Intent. Alas it is in Troytown. The nearest human life is out of town from the King's School, or behind the Watts Almshouses - an area of outstanding natural property values. But I think there may be some small squares in that area with unrestored houses that might fit your bill (probably no trees).

Try Ridley Road, The Close, Watts Ave, Roebuck Rd, King Edward Rd, Ahbert Rd, Albany Rd, Baker St. I thnk most of the houses will be too big. The cloisters, love lane, etc are nice but very dear.

Don't take Dead Horse seriously, there is no nice part of Strood. There are also no folk sessions in Strood.

How about Lower Rainham? I think there are still some sessions there.