I refer to £1 per Tier Point (TP) as the Holy Grail for British Airways Tier Point Runs.
In my (now slightly outdated) guide I pointed out that American Airlines domestic first class is consistently the best way to haul huge amounts of TPs in a short amount of time. This changed in January this year when American Airlines changed the booking code of domestic first to be aligned with those of business class elsewhere. Still it's a great deal, but just not as good as before.
British Airways is an oddity in the sphere of loyalty programmes. It spans two airlines and a separate non-airline entity, and to earn higher levels in the programme you will need to earn TPs by flying on BA or its partner airlines which are not directly linked to the length of routes you fly. (See the Avios and TP calculator here)
Currently one excellent source for TPs is Malaysia Airlines especially their intra-Asia and domestic routes. There are a couple of fares stands out amongst the rest.
Kuala Lumpur to Penang, priced at £43 one way or £78 return. Each leg yields 40TP so on the return fare you can get £0.975/TP. This one is nice as the gate-to-gate time is approximately 1hour, so the airborne time is somewhat less.
There is a 2-day minimum stay requirement for return tickets, but the fare works in both directions so you can plan outbound and return legs using two separate tickets. If you want a quick turnaround, you will need to book as one way fares. (Please also see Joe's comment below for his experience with Malaysia Airlines using nested tickets)
Taipei to Kuala Lumpur is 2012 miles, a smidgen above the 2000 mile threshold to hit the 140 TP you get from long haul business business class.
Taipei to Indonesia (Jakarta or Bali) priced at £412, or £1.14/TP. (found on Malaysia Airlines' Taiwan Deal of the Day page. You can save it by dragging and dropping it into your bookmark bar.)
You can search for both fares on Malaysia Airlines homepage.
You must remember that to qualify for BAEC Silver or Gold status you must have at least 4 BA flights within the year. Therefore doing these Malaysia Airlines runs in themselves will not suffice. However, if you can buy the cheapest and shortest Hand Baggage Only fares in economy class, typically about £30 to places like Amsterdam, Malaga, Brussels, Luxembourg, or domestic UK Routes then this would be the most economical way. You can see the cheapest routes here.