I've been through this with my DD15.
CAMHS were useless - we were supposed to get an urgent 24 hour call back after her school referred her when she self harmed at school.
That call finally came after 6 months.
We'd already been on a waiting list with child psychology at GOSH for a year by the time she started the self harming.
We were lucky in that DH has health insurance through his job that also covers the kids. In desperation we called to see if they could help with DD self harming and they agreed to a private referral to a psychiatrist who recommended counselling and eventually gave us a prescription for propanolol and then fluoxetine.
I believe the appt with the psychiatrist would have cost £350 if we'd had to pay for it and the counselling is £80 per session ( thankfully covered by the health insurance otherwise we'd never have been able to afford it )
It's taken a year but she is now so much better thanks mainly to the fluoxetine. Feel like we've got our little girl back.
A friend of mine is going through similar with her DS and paid the £350 for the private consultation and came out with a prescription for fluoxetine.
We were more reluctant to take a prescription and wanted to rely on counselling/therapy first but we eventually realised she needed medicating. Wish we'd taken the prescription earlier to be honest but we are cautious people.
Hope you get the help you need.