Telwebb.
depending on exactly what you want to do, on whether you are organising this or it is part of a parent organisation, there could be several options. Sorry that does not help much, but I don't know what you have in mind.
If you are purely thinking outdoor stuff then it may be worth contacting Bristol City council or South Glos council. For many years Bristol have run lots of outdoor things, both for school/education based stuff, as well as D of E.
The local (South Glos) local education Authority (LEA) are also a good point to start with. I mention these start points, as you mention 'qualified' so you will need an organisation that can not only have a track record, but will also have all insurances, case models for you to study, and be current with all staff for CRB checks too. Plus they (if they help) will also be recommended for instructing kids. I say this, as although I have qualifications and insurances for my day to day trades, I need council approval to work in schools or with kids.
It may also be worth contacting the Barton centre (near Compton Bishop), who run lots of kids activities, and have accommodation.
Near to Charterhouse is the Mendip adventure centre, which you will be able to get details from, from the above sources or from the mendip warden service.
Just a few suggestions for organisations with several decades of practice in running kids outdoor activities.
Edited to add: these are all very local to you, as I fully understand the price of hiring approved seat belted coaches for kids, and how this bumps the price up for any planned trip.