On the private/charity angle, do therapist there work on a sliding scale (charge by different rates by ability to pay)? If so, you might be able to get your S seen for not too much out of pocket.
If you can't get your S in through one of the programs that will foot the bill, and you can't afford it on your own, again look at a local university. See if there are any departments with masters in the relevant fields where they specifically train counselors to do children's therapy. Inquire if they know of any good programs that they can refer you to that you can afford. Often they have something set up to give their counseling students hands-on experience (at least this is how it is done here in the states), and as this is always done under direct supervision (usually for true beginners the supervisor/instructor is looking on in an adjacent room, & for more experienced students, they review the tapes and give feedback that helps with the next meeting), the quality is usually very good.
Me: 50 W:43 S6, S3 M: 12 yrs. T: 17 M is bad & Not happy Bomb Mar '14 S 5 Feb '15 D Bomb 13 Apr '15 (but "no hurry") DB Coach May '15 Wants proceed on D Aug '15 Starting 1-on-1 negotiations Sept '15