note that contracting requires establishing and maintaining relationships. there are also legal implications of messing stuff up. working for a consultancy shields you from all of this.
What relationships? In the UK, most people find contracts on job boards. You just filter by "Contract", instead of "Permanent". After that, there's a job interview etc. The advantage of being a contractor is that the interviews are much more relaxed and there's no HR involved in them at all.
Tax and accounting is easy, a good accountant for c. £100 a month will cover everything for you such as payroll, any accountancy questions and preparing your end of year company tax returns (CT600) as well as your personal self assessment each year. Honestly the most I have to do each month is send an invoice to the client which takes about 10 minutes and tag a couple of business transactions in FreeAgent every couple of weeks.
Keeping a pipeline of work is obviously the trickier part, but once you get your first couple of contracts (probably via a recruitment agent) then you quickly build up a network of other independent contractors you can reach out to as well as any other permanent members of staff you worked well with who have moved to new roles etc.