Hi, Welcome ad enjoy the SWCP.
It is unlikely that you will find anything around Heathrow. Head down the M4/M5 to Minehead (or you could go to Swanage) You will find suppliers of camping equipment in those towns. If it is gas, rather than a liquid, that you are looking for then the challenge is to find a canister with the same connection as your stove. Whatever you are able to buy in Minehead or Swanage will be available along the SWCP with a bit of forward planning.
Good Luck and enjoy
Robin