I am an Indian Citizen and US green-card holder. While returning from Mumbai to USA, I will stay 2 days in London for a short trip. But according to the scheduled arrival and departure time of my flight, it would be little longer than 48 hours (≈ 50 hours). Since for a transit visa the stay should be within 48 hours, can I pass through the immigration control after 2 hours of landing and go for a transit visa? I'm not sure how they would count the duration of my stay in London: would it begin from the scheduled arrival time of my flight, or from the time I'd go through the immigration checkpoint? Any suggestion would be greatly appreciated. Thanks.
What's likely to happen if you try this is the following. While checking in to your flight in Mumbai, the airline officials will need to check that you have proper passports and visas for your destination. They're going to be strict about this because in general, if you are refused entry, the airline that brought you in is responsible to take you back.
They will see that your onward travel from the UK is not for 50 hours and their computer system will probably tell them that you are not going to be admitted to the UK.
If you do get on the plane, when you land at Heathrow, there is no real place to hide out for two hours before going through immigration.
In other words, you have to convince both your airline and the UK immigration people to make an exception in your case, which is not very likely.
Therefore, I suggest adjusting your travel plans or just getting a UK tourist visa.