Looking to Swap to 3 - 4 bed house, for 3 bed flat inner city London

Hi, we have a three bedroom flat, with an allotment space in the front where we have grown many vegetables. We have the transition 5 minutes away, the bus route 2 minutes from the door, next to two art galleries, and University Arts London. We have easy bus routes into the inner city to Westminister, the borough of city London, Angel Islington, Holborn etc. We have one under-stair storage space and one smaller one near the door. Living room, connected to dining room. We are next to several schools, Harris Academy Peckham, Goldsmiths Primary, St Georges Primary etc. We are looking for a 4 bedroom house, to accommodate my mother, and children. Hopefully, with a garden. We would ideally like the area to be Dartford or Graversham, but we can accommodate for most places.