We stayed at Abbey Wood, you can get bus from outside the site right into town, or there is a station about a 5 minute walk, it is ideal for central london, or Greenwich is also worth a visit.
For me it would be Commons Wood at Welwym. Open 12 months a year direct train service to Kings Cross or Moorgate and easily accssed from the A1 , M1 and M25. Not in London but not to far.