No, I actually did not mention India or Pakistan. The Middle East generally includes Saudi Arabia, Syria, Libya... etc. It does *not* include India or Pakistan.
I know that India and Pakistan are on the southern part of the Eurasian continent, but typically, those are different ethnicities than the Middle East or Asia. India has several religions, plus the caste system; Pakistan seems to have a lot of Muslims. If you look at racial subgroups, the Pakistanis and Indians have more in common with each other than they do with European Caucasians, although all are Caucasians.
I think the British usage of "Asian" to mean anyone from east of Russia is highly confusing, even though that part of the continent is classified as Asia.
Mutual misunderstanding there - I assumed that your original post referred to Pakistani etc Muslims as ‘Middle Easterners, since few British Muslims come from the Middle East - most are from Pakistan, Bangladesh and to a lesser extent India.
The origin of the British ‘Asian’ usage dates from the days of the British Raj, when the only people from the continent of Asia seen in any numbers in Britain were Indian. ‘Asian’ wasn’t then - and isn’t now - used for the Far East of the continent.
In 1971 the West Pakistanis (what is now Pakistan) killed 1 million Bengali Muslims in East Pakistan (what is now Bangladesh) and Bangladesh went for Independence.