I am from India going to Bangor, Wales for higher studies and my destination airport is Manchester via London Heathrow.
Do I need a transit visa?
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"Transiting" means entering a country only for the reason of changing planes etc. to continue on towards your destination in a different country. For example, if you flew from India to Germany and then immediately from Germany to the UK, you would be transiting in Germany.
You are not transiting in the UK because, the UK (England, Scotland, Wales and Northern Ireland) is one country. You are going to London only so that you can take another plane, but that second plane is not to a different country.
The visa that you need for your studies is the only visa you will need to enter the UK.
Bangor, Manchester and London are all in the same country (United Kingdom), so A visa that will allow you to get in to the UK should be useable for any method of entry, specifically it shouldn't matter if you enter in Heathrow or in Manchester.
I also believe you'll go through immigration in Heathrow, and the flight to Manchester is a domestic route.