With student finance, you're eligible for funding for the new course length plus one year, minus any years of previous study. So if you take one year at Surrey and then change to any other uni (whether London or not) you'll be eligible for full funding for the whole of the new course, because you have a spare "gift year" to cover it.
If you decide to study another year at Surrey and then change elsewhere to complete the full degree, you wouldn't have enough funding.
If you study one year at Surrey then change to another degree, but then change your mind again and want to restart, you wouldn't have enough funding.
Taking a gap year doesn't affect your eligibility. You are far better off taking a year out to improve your mental health and decide what you want to do. If you change to a London uni and it turns out to be a wrong decision, you wouldn't then be able to change your mind again and restart unless you can fund it yourself. So don't rush into anything.