I've been in London for 6 years, I've contracted for 5 of those (architect position at the BBC was "only available is it was full time". In hind sight, I shouldn't have taken it). I've been out of work for a total of 6 days in 6 years (took a week to get a contract after a 3 month holiday). I started my first contract within 6 days of landing in the country (nothing prearranged)
Freelancing is when you go from short term contract to short term contract, or you quote/bid for work. They can be 2-5 days a week, for maybe a month or less. For that I agree you need to pimp yourself like @jangosteve says, because you are moving so much. You are basically a 1 (wo)man consultancy.
I don't do this (except for my "on the side" mobile stuff). Too inconsistent.
But if you are a back-end dev (or front end, just to a slightly lesser degree) you can stay in the same place for _years_, or until you get bored of it. 3-6 months is a normal minimum, at least in the .net space which I'm in.
Unless you are useless. Then you're likely to get turfed out quickly.
Where I am at the moment, I've been there for 3 years (nearly). Last place I was there for 2 including some as a full timer. I've done moonlighting (apps, websites) at the same time. One of the guys I work with has been there for 8 years. I'm sure HMRC should have something to say about it, but no one is looking.
I'd normally want to move on after 2, just to keep fresh, but I do the same with FT jobs.
I'd be very hesitant about taking a FT position anymore. You can be fired with 1 months notice, and you get 4 weeks holiday, and maybe 75% of the wages _with tax removed before you get it_.
Contracting, I get no notice (this has only happened once when the customer literally ran out of money), but usually 28 days. I don't get paid if I'm sick, but I keep myself healthy and allow for 2 weeks sick and 6 weeks holiday a year. I have insurance to cover if I get REALLY sick.
I usually take closer to 8 weeks holiday a year. Sometimes between contracts, sometimes during them (usually during, but not at the same time)
For me, contracting is an easy way to work. The paperwork overhead with a system like freeagent is TRIVIAL if you have a half decent accountant (cough mine is great cough maslins.co.uk). Make sure you have a bit of a buffer in case you DO have issues getting work or a client pays late (if they pay late consistently, fire their arse)
So: 1. Get a limited company, and a good accountant 2. Get indemnity insurance (you need it anyway) 3. Get used to being called by recruiters who you'd like to slap with a fish 4. DO IT