I used to work at Kingswood / Camp Beaumont.
Children always appeared to enjoy themselves and settled in fairly quickly. Obviously there was the odd bout of homesickness and it's better not to ring home as it makes it worse but they were mostly soon distracted. Generally the only children that had calls home were those there for multiple weeks or who could not be settled. Lots of children were there whilst parents holidayed elsewhere, were working or children from overseas sent for the full 6 weeks to learn English.
Each group had two group leaders who stayed with them during the activities, are with them at meal times and got them sorted at bedtime same as teachers did on a school trip. The group leaders stay in the ensuite room a the end of the corridor and female / male will supervise their own sex dorms. They will practise fire drill on the first night and if it goes off during the night group leaders do room checks and ensure they are clear during evacuations
Activities wise you need to look carefully at what is on offer some sites are better for older children others for Primary and the activities reflect that.
Most group leaders are taken on for the summer before Uni starts and are mostly 18 years olds or returners. Some will stay on and become an activity instructor doing an apprenticeship during a gap year. Activity instructors were also under 21, a mix of UK, Australia, New Zealand and South Africans when I was there.
Senior instructors, logistics coordinators, duty instructors likely 22-25 having stayed on after completing their apprenticeship.
Centre Manager, Chef, Estates management and Cleaning manager were all 'proper' adults. However although instructors are young most have held roles of responsibility in cadets or scouts and sports groups.