This thread should answer most of your queries
http://www.flyertalk.com/forum/briti...lounge-10.html
I did the GOA > BOM > LHR trek at the end of November. Despite landing at BOM around 8am it was almost 10am before I reached the International terminal so you tend to be thankful for the long-layover!
Print your boarding pass out at the hotel to present to security at the International Terminal entrance, an itinerary didn't seem enough for them. The whole check-in experience and lounge are wonderful and I was able to access straight after check-in around 10.30am.
Enjoy!