Years ago when I went to see Leicester Tigers play I remembered reading an article in the match program about a forthcoming friendly between the Tigers and the Indian national team. Was as close as you'd expect.
Think the city of Leicester is a case in point, actually. It's possibly the only major city in the country where union is bigger than football and has a large Indian community but I can't recall one Asian player ever breaking through to the Tigers' team. There just doesn't seem to be the interest there.
The only British Asian to play top flight rugby of either code I can recall is Ikram Butt
who actually played league for England. He's of Pakistani rather than Indian extraction tho.