Hi, I am a tutor, I teach secondary maths. I left full time teaching to look after my children and now tutor in the evenings and a couple of afternoons whilst my youngest is at preschool.
I don't have insurance, though I am looking into it. I don't tutor at my own house, which makes a difference, but feel I should have something to cover me if someone is not happy with my work. Not happened yet but still! So that's something I will be sorting out in the next couple of weeks.
I am also in the SW, and prices are lower here. I charge £20 per hour, rising to £25 if I have to drive over 5 miles. (To be honest, the two tier system is a bit of a pain as it means having to establish driving distance before finalising a price, and I will be charging £25 across the board in September). This is a bit over the average for the SW (about £19 according to First Tutors website) but I am a qualified teacher with a lot of A level experience, and I also mark exams in the summer so have a lot of experience exam wise. Pricing is a tricky business as too high and you will price people out of the market, but too low and you look inexperienced!
I have never gone with an agency, I've always found it much simpler to organise things myself. I can't see any benefit to using them, they don't make the business of finding clients any easier (in my opinion) and they will take a percentage of your earnings. There are websites where you can advertise your services, usually free of charge, and they are well worth investigating. You can see what others in your area are charging as well. First Tutors and the Tutor Pages are two that come to mind. However, once you have a few happy clients then word of mouth is by far your best form of advertising. If you have contacts in local schools then they may be happy to pass your details on if asked (some schools won't do this).
I have a DBS though I have never been asked by a client to show it.
The only down side I can think of is that most of the work is evenings and weekends, and whilst this is great when the children are at home, now they are at school it does mean a bit of a rush in the evenings, and cuts into family time. I am strict about my hours and often have to turn people away in order to keep some family time. But otherwise I love it, it's very flexible and keeps me in the education world on my own terms.
There is also a Private Tutors group on TES which is very useful. Let me know if you have any other questions, I'll try and answer!