Quick follow-up - is the Greene King IPA league always the league to and from which teams are promoted/relegated?
Yup,
The English leagues are structured so that, theoretically, any club could be promoted from the lowest lowest league all the way to the premiership, and vice versa.
The premiership does have a bunch of hoops to jump through for clubs being promoted into it though - certain stadium regulations (seating numbers, safety standards etc.), which can be an issue for clubs wanting to get promoted (London Welsh, for example, had to move from their ground to share with a football club as their grounds only held 7,000 and the minimum standard is 12,000).
It goes:
Premiership
Championship
National League 1
and then from there it starts branching down, so there's National League 2 North and National League 2 South, and it keeps branching out until you get leagues like Midlands 5 West (North)