The term commonly accepted as polite in Britain at the moment is the somewhat inaccurate "Asian". This usually covers people of Indian and Pakistant descent, and it's a term they often use themselves. I think the problem with the more obvious words is that "Indian" suggests American Indian to many people. Also, the people in question are more likely to be Pakistani, and the term "Paki" is now often used by racists as a term of abuse, like "nigger". Thus the term has become tainted with these racist overtones.
"Asian" ia pretty silly because there are also lots of British people of Chinese/Hong Kong origin, who are also "Asian" in the geographical sense. These groups are increasingly being referred to as "oriental", which is also a bit vague....