Somewhere like Barmouth in North Wales is readily accessible by train from the Midlands (a long but extremely scenic journey!) - we used a large seafront house booked through friends which my daughter organised (although it was a nightmare with people dropping out last minute). However I did arrange to be there myself in the background - I had friends stay with me there as well for a couple of nights each, and although I drove with a carload of initial supplies, most of DD's friends got there by train and they sorted most of their catering collectively. (we did organise the food for a "prom on the prom" as a couple of her friends had missed out on their own school prom and wanted to dress up for an evening)
I doubt many venues would accept unaccompanied 16-year olds (look at the bad publicity there's been about drinking in Newquay etc) and DD at 16 was happy enough to have backup. At 18 post A level she went back to the same venue with another group without me!
But if you have no useful friends with a spare seaside house (I think they've sold it now!) how about Youth Hostels?
https://www.yha.org.uk/ - several in outdoorsy places, accessible by bike/ train. Might be booked up for this summer though