I beg to differ.
MPs has specialised teams of assistance in their surgery, responsible for immigration matters. Their is a special MP liason team at the UKVI. These officials are paid for by tax payers money, so I do not accept they are just doing it to get votes.
MP have individual and collective responsibilities for individual constituent and the constituency as a whole.
If a member of their constituent encounters issue with the executive, which in the UK is linked to the legislature, as MP can be both legislature and executive, which is headed by a government member of Parliament or Lords, then it is their role to address it.
I may be wrong, but it is an interesting point for people who know the role of their MP.
https://www.parliament.uk/about/mps-and ... mbers/mps/