How do you find a good tutor?

I'm a tutor. I agree with others. Word of mouth.

Qualifications, experience, DBS are all good. Ideally, you also want a qualified teacher that examines and teaches the A Level that your son is taking. An examiner will have exactly the information on what is needed in order to pass that exam well. A teacher is needed because they will have experience of the areas students usually struggle with and will have a range of teaching strategies they can utilise. However the best person on paper isn't necessarily the best tutor.

Equally, do not low ball it and look for cheap. You'll be wasting your money and your DS's time.

I'd imagine science tutors are scarcer than my subject, and I earn £65 an hour. So you're probably looking in the region of £70-80 an hour. So if you're paying that you want someone good.

Have you tried asking his school teachers? They may have teacher friends who can help (from other schools- you are usually not allowed to tutor students from your own school).

I've been tutoring A level biology for over 16 years. I have a first class degree, a PhD and a 15 year research and academic career behind me. I do not have a teaching qualification. It is extremely dismissive, and frankly ignorant, to think that you have to have a teaching qualification to be an excellent 1:1 tutor. In fact, one might conclude that it's an advantage because we aren't institutionalised and we don't talk to our tutees in a 'school-like' way. I have had to provide an enhanced DBS, my degree certificates and references to be on tutoring websites, so no, not exactly 'completely unregulated.' School teaching isn't exactly regulated either, if we are looking at subject specialisation, deep knowledge and talent. On the other hand, if we are talking about undergraduates tutoring A levels with, I'm on your side...I cannot fathom parents paying for this, other than they are cheap.

What @Deneke said.
I found this website when I was looking. They are all qualified teachers and you can read a lot about them
www.teacherstoyourhome.com/uk

I have a word of mouth maths tutor for maths and I had to go to pmt.education website for a science tutor. My DD is in yr10 currently and has grades increased with both.

Try the pmt.education website, you can see each tutors’ profiles (many are teachers).

Unfortunately tutoring is completely unregulated. Anyone can offer tuition without any proper subject knowledge, qualifications or teaching skills. Even tutors from tutoring agencies often lack those.
I am a qualified maths teacher and it always baffles me that some parents are willing to pay people who are unqualified and lack relevant knowledge and experience.
Look for the following...
Qualified teacher status (eg a PGCE certificate or equivalent).
A degree in the correct subject.
Experience teaching in real schools.
Experience teaching and/or marking the exam board that your child is studying.
Don't be tempted to book someone without those to save on cost as you'd just be wasting your child's time.

Usually local word of mouth. You're leaving it a bit late. Try to get one now and start asap