So ... financial situation is basically neutral in the short term, and longer term variables re: career advancement also cut both ways. I would just set that aside and think about what will make you happier.
For me, work-life balance is at or near the top of the list. Living near friends and family is also a big component of my happiness, but if you are too busy to see them, or stressed out so you don’t enjoy your time, then proximity doesn’t do much good.
One other thing to think about: Sounds like you could rent in Manchester for a time and save even more money than in London. You could try it on for a year or two and if you missed London, you could move back without the anchor of owning a home. If you like it, there will still be homes for sale in a year or two.
Good luck, it’s an exciting branch in your life!