Whilst you are looking for a tutor, a number of people have recommended the Khan Academy. This is a site with free online video tutorials on various subjects including lots of maths. https://www.khanacademy.org/
He is currently predicted a C but the sixth form says he has to get a B minimum to get in. The school and 6th form are all about the results. His school is like a machine. I would prefer a tutor just to get him back on track with the elements he feels he is weak at.
There are various online agencies. The Tutor Pages is free for customers - tutors pay to advertise and have to put some effort into their profile. I used to get quite a lot of work from there, and hardly any by word of mouth (which is not because I wasn't good, lol, I was very successful. The idea of a school that had several pupils in one year going to the same tutor sounds awful - did the school know? I always told people to talk to their school first before paying me).
My ds gets on very well with lessons from www.mathsdoctor.co.uk/ - their prices are variable depending on how many you have, I'm not sure it is worth it for the starter package but the other ones might be depending how much you want to do and how well your ds gets on with a computer.
My DD has one other boy in her class going to the same Tutor, and the other "top" student in the class also has a tutor. We've recommended DDs tutor to a number of people. I have talked to school and had some free tutoring in school in the past.
Admittedly everyone is very open about Tutoring around here (if you can afford it). And I know DD's Tutor also teaches girls from the highly selective Girls school. But some of these are being Tutored to get A/A* not just Cs and Bs. DD has gone from worrying about passing GCSE to choosing Maths for A'level (she's even considering further Maths). Her confidence has rocketed, and she learns much more in 1 hour of 1:1.
We have a similar situation to mummy time. DD is y9 and we had a tutor during Y8 when he could fit us in (excellent tutor, this is his full time job and he's very busy) as dd was at the bottom of the top group at the end of Y7 but the teacher wouldn't move her down a group as dd has the ability but takes a bit longer and lacks confidence. During Y8, with his help, she progressed easily, and now in Y9 she's sees the tutor weekly. DD is loving maths (she says she's near the top in the group now) and talking about carrying it on to at least AS level. That hour of 1:1 focused time makes an amazing difference, & it's worth every penny to us.
I would also recommend www.Mathsdoctor.co.uk - my dc have both benefitted from their online tutoring. eldest dc especially enjoyed the online format. Which reminds me I need to book up some more lessons for her as she's nagging for more!
I have used UK Tutors and First Tutors in the past. They are both online sites which allow you to contact tutors on your area . You pay them a small fee (£20 I think) once you have accepted someone as a tutor.