I hear it takes about 12-14months for Heathrow and about 10months for Gatwick, obviously depending on your ability. Ive also heard the chop rates for Heathrow arent far short of that for Swanwick, but Gatwick is a bit better (Correct me if im wrong anyone).
Given the current climate at the college regarding failure rates (given that only 2 people out of 10 on the current Area Advanced course are 1st timers through!) i think it's a far more sensible option to ask for the Aerodrome option as there is a much better chance to validate (and far sooner) than if you get sent to Area. Also, dont expect EGLL or KK to be taking people. There are the other London airports, City are always taking and i hear Luton are short.
Also, if you're interested in having the flexibility to move around the country (and the world), then getting the additional Approach ticket after Aerodrome is definately worth it (And the Approach course is fantastic). If you fail anything practical on the Aerodrome course, it usually means automatic Approach.
Objective one: Get through the college, Objective Two: Validate.
One step at a time, but as i say, with the current climate, far better to request the option thats most likely to see you validate! Unless you have a craving for Area. Hope this helps.
Any questions, pm me.