The NHS have confirmed that they'll be offering autumn boosters to anyone over 50 + health and care workers and the clinically vulnerable.
People in care homes, health and social care workers are the first priority, then the 75+, then everyone over 50. They also allow for "self declaration" of carer status or "living with at risk person" etc in that later category so I think the categories will be pretty broadly drawn.
All boosters will be "bivalent" - that is they'll have components that trigger antibodies to the original Wuhan variant and to Omicron. Currently that would mean all Moderna (because that's the only bivalent vaccine approved) though they don't say that.
In England - rollout in the care homes is due to kick off in early September, over 75's should get contacted by the NHS for appointments later that month. They'll be followed by the 65+ and the clinically vulnerable, then anyone else who's eligible. The intention is for everyone who is eligible and who wants it to be able to get it by the end of November. The notification letter to the NHS trusts says the schedule might be accelerated if supply is there and pressures on the NHS justify it.