Bloody-mindedness mostly.
I worked permanently for various companies in and around London for about 10 years, then got sick of London, moved to Australia, did a couple more years permanent work there, then decided to move back to the UK. At that point I was sick of being an employee and had a vague offer from a friend to help bootstrap a startup, which fell through. So in lieu of having an idea to start up a company myself I decided I was going to be a contractor, set myself up a limited company and started throwing my CV at anyone that asked. I have got most of my contracts through agencies that called me, not through contacts.
Making the leap can be tricky - if you have a notice period longer than one month you may have to quit your current job and then look for contracts afterwards. A lot of people want contractors to start now. You may not find one for a month or more, I've had dry patches lasting a couple of months before, and it might be another month after you start before you can invoice, and it could be another month again before you get paid, so you need a financial cushion.
As soon as you get your first contract you'll need an accountant. These come in at about £100 per month. I use Nixon Williams, this is not necessarily a recommendation, they deal with hundreds of contractors, the service is streamlined but pretty basic and if you need anything out of the ordinary they probably won't do it.
Errr.... time of year may have an effect, like a lot of things it seems to be easier to find work in the first few months of the year, though I have had two start in November/December.
Anything else you want to know?