The other day I found my son a local maths tutor through First Tutors (an online tutor matching service). I had no idea that there was so much choice in this area of the market! Schools should really inform parents of this kind of thing!
Like the comment below I also registered with several other sites too (tutors4me, UK Tutors and Tutor Hunt) but they had no really suitable tutors and no reliable feedback from real people to reassure me. Additionally there didn't seem to be any form of responsive customer support for the others (or even a company number / registered address for UK Tutors - be very careful here as they take payment), while First Tutors dealt with my (admittedly easy) question very quickly.
Everything on the First Tutors site was quick and polished, I ran a search, contacted 4 tutors, and within the day had found a suitable tutor and bought his details! Everything is going well and my son is enjoying his tuition (only had 2 lessons so far) and we are satisfied with his progress.
First Tutors is not free for parents, but the price scales depending on the price of your tutor (£4.99-£19.99, £14.99 for me) to keep it affordable for all, but it wasn't really clear how this was calculated (or at least I couldn't find it).
If you are looking for a private tutor anywhere in the UK this is the site to use!