At EU/EFTA airports it is the airport that is responsible for assisting passengers with reduced mobility (PRMs). So in Scotland and any connecting point in the EU it really doesn't matter who you travel with. Despite this it is the airline you must notify that you require assistance. It is best to do so at time of booking, there is no reason to do it any later.
For assistance at other transfer points, and in particular in Pakistan on your return, it is the airline that is responsible. Check their web sites carefully to understand what they can and cannot do.
In the EU the airport must provide assistance if requested, there is no test or qualification.
From personal experience, with an elderly relative, I would avoid Gatwick.