Those with state schools with free clubs (Mrz, not sure if this applies to yours) - there is a charity www.chessinschools.co.uk
which provides chess lessons in schools. Possible it's organised through this scheme?
Otherwise, as we've said above, you are either looking a a chess playing parent or volunteer giving up their time for free, or a nominal charge, or a professional coach who makes a rather poor living out of chess coaching.
Chess seems to be a strange world. There is so little money, despite the amount of time and effort, and huge talent, it takes to become an international level player, that many players coach or commentate on live games to make ends meet.
Also, the world of junior chess is very competitive. I've seen parents pay for coaches to stay over night at hotels during tournaments, so that they can coach in between rounds.
So, £6.59 ph might be a complete rip off, or it might be a bargain, depending on the coach!