Hi. A little different, but I left the local authority to set up in practice as a private educational psychologist a couple of years ago. I am so glad that I did. It's daunting at first but the best professional decision I have every made.
Here are some ideas:
The BPS does a training workshop for practitioners thinking about setting up in private practice, which may be worth attending.
There is the BPS Independent Practitioners forum (email Carl Boucher to join) and the newly established IP SIG within the BPS. It is also worth making links with other psychologists you know who work independently. I have found that most are happy to share ideas and information. I also have a number of friends and ex-colleagues who I use for cross-referrals
I eased myself into private work by working as an associate for 2 more established private practices, which gave me the confidence that I was 'doing it right', a good level of supervision and an idea of the sorts of issues that need thinking about. It also gave me an idea of how I wanted my practice to 'feel' to clients, where I wanted to focus my practice and how to do things differently (where appropriate) to more established practices. Alongside that I gradually established my own client base and now work mostly for my own practice. I guess that you can also look at private healthcare providers to give you a steady income stream, although it can be a bit of a headache, as I understand!
You will need a good supervisor. One of the nicest things about working privately is that I get to choose a supervisor who is compatible with my ways of working. I also like being able to choose my CPD and am using some of the time I have freed up from the (relatively) better income to begin my training in Systemic Psychotherapy. The BPS has a list of approved supervisors.
It also really helps to know someone who runs their own business (any sort of business) who can explain the ins and outs of tax returns etc. It's quite simple, but daunting at first. I use a small business accountant, who saves me more money than I spend on him!
Best of luck, I hope that helps a bit. :)