I called British Embassy in NewYork and enquired about AP, Passport with GC stamping, Plastic Cards (GC), US Visitor's Visa.
I talked to a guy named Neil and he was generous in replying to my questions. Here are his answers,
1) AP People do require transit visa.
2) To my surprise, he told me that you require transit visa, even if you have stamping for GC in your passport. Does anybody else also enquired about the same.
3) People having physical GC (cards) do not require transit visa.
4) People having valid US visa (even if that is Visitor's visa, like for the parents) do not require Transit Visa.
Regards,
feb12rd.