Simon said:
No, Bristol is closer but Heathrow is the biggest / main airport so you will probably fly into there. If you plan on flying into Bristol and can't get a direct flight look at flying into one of the other regional aitports like Manchester or Birmingham.
You can often save money by flying to Bristol via Amsterdam Holland rather than direct to Heathrow. This route is operated by KLM and NorthWest and has the advantage of being cheaper and getting you closer to WSM by landing at Bristol.
Englishman.