Take it from a Londoner who has also lived in Manchester: I think the latter provides a MUCH better experience for students!
There are 3 big unis in Manchester, which allows you to be part of a great student community. In London, the proportion of students to general population is way smaller.
Everything is much more expensive in London: accommodation, food and drink, restaurants, bars etc. Also, Manchester might be smaller than London, but there are so many bars, restaurants and shops packed conveniently into one nice, area.
I also think the people in Manchester are a lot more chilled, friendly and easy to get on with. In terms of the students, there is a great mix of people from all over the country with different backgrounds.
Honestly, I would be shocked if you went to Manchester and found you still hated it after a couple of weeks there. One of the best places to be a student!