I run a full-time tuition business (me plus two other tutors employed by me at present). I've been doing this full time for over 4 years and part-time for over 7 years. I'm also an examiner in my subject.
As noblegiraffe has stated, year 10 is definitely not too early. Tuition is not about intensely drilling students with the "right" answers (I certainly don't do that) and nor is it about teaching "tricks for ticks" in exams. It is about supporting their learning and therefore helping to ensure their lessons at school are as effective as possible. Often it can be about increasing a child's confidence in the subject because they feel "safe" to ask questions that they don't dare ask in front of their classmates. It's also just giving that one-to-one attention and personalised feedback which teachers simply don't have time to do due to the (many) other pressures of their jobs. When tuition works at its best, the parent facilitates communication between the teacher and the tutor so that the tutor knows exactly what a student is working on at any time and the teacher in turn receives info back from the tutor. Not all parents like to admit to school that they are using a tutor though.
Ensure the tutor has had relevant background checks (enhanced DBS and/or national police record checks), has experience in the subject area and with the exam board specification and that the relationship between the student and the tutor is positive - they will be working closely together, so their needs to be trust there but this trust takes time to build up.
Whilst some tutors can be insanely expensive (£100 p/h +), also bare in mind that you often get what you pay for. Experience and knowledge takes a long time to acquire and should not be undervalued. A £15 p/h student may seem like a bargain, but how much experience do they actually have? Do they have the necessary checks/paperwork/insurances? Will they put in time outside of the contact hour to ensure their lesson is adequately prepared and they have suitable resources to hand (you don't want a tutor who just blindly works through the textbook), or to feed back to you? If they are travelling to you, would you be comfortable paying essentially less than minimum wage for someone's expertise? Remember, many students are still in the stages of exploring the subject themselves and their thinking within a subject may be at times naive or not fully developed and they are more likely to pass misconceptions on to their tutees.
Are you willing to travel to a tutor? (which will likely decrease the lesson fee), if not, consider online tuition in order to increase your pool of potential tutors, especially in shortage subjects like maths.
Good luck finding someone suitable and I do hope that my rambling helped somewhere along the line.