The Girl Guides and Girl Scouts run a hostel called Pax Lodge in Hampstead, North London. They're very experienced with that age group and many volunteer staff members are 18-20 years old, have some fun activities for that age group sometimes, and no one in your family has to be a member of scouts or guides. All are welcome.
https://worldcentres.wagggs.org/pax-lodge/
There's a button at the top to book a room and the whole calendar scrolls down.
It's right next to Air Studios, several main buses stop at the corner, and a pub with good dinners is right across the street. There's a kitchen for guests to use, and there's a grocery store 2 blocks down the hill. THe buses that stop at that corner were at least #24 (to Trafalgar Square) and 268 and 168 (to the Southbank and more). They all went through Camden. Popular shopping place for the volunteers and staff.
This is a video of the walk from the bus stop at the corner (where Air Studios is) to Pax Lodge's front door.
https://www.youtube.com/watch?v=ODGdarKAOcU
I've volunteered there in 2011 for 2 months, and now I volunteer on the World Foundations for Girl Guides and Girl Scouts' committee Friends of Pax Lodge.
There were many renovations done recently, and there's also coin operated laundry machines available for guests as well.
-Alison