Doesn't have anything to do with the Milesian records ~ on the other hand it has more than a little bit to do with the fact that English-speaking Welshmen with a brogue were a big hit in the British colonial service in the Raj and constituted a major percentage of the staff. They frequently stayed on after their government service to teach English to the native people who wished to advance.
The Welsh accent is now imbedded in the tongues of those Indians for whom English is a first-langauge (and there are tens of millions of such folks).