@mah94,
How much you need to save depends on how you live and how long you expect to remain unemployed.
You haven’t said that much about yourself other than being gay.
What qualifications you have?
You may have skills more suited to the North or elsewhere.
You talk about the UK, but all the places you mention are in the South of England. No mention of Scotland, Wales, Northern Ireland or the North of England in your reply.
I would be very wary of moving to London without any job offer or contacts. You’re from a rural area, and London is huge, bigger than New York.
Brighton is the gay capital of the country, but that causes its own problems with people moving there purely for that reason and being exploited.
Do you know anyone in the UK?
Do you have any contacts at all?
Moving to the UK with no job offer or contacts is a recipe for disaster.
Btw, Reading is a bloody shithole.