1) When you are self-employed, you don't have to 'put money away' as such - you just don't receive any income during the period that you do not work.
2) As CC suggests, there is ambiguity in your question over who your boss will be. I guess that you work for an end client and your boss is an 'agency provider' of some sort. If you are going to establish a contract with the end client, invoice the end client, and be responsible for paying your own tax and NI, then you are self-employed. But have you fixed this with 'your boss', who is currently presumably making a profit marfin between the rate you are charged out at and the rate you get paid. Or are you going to find yourself your own clients.
3) If you do propose to do self-employed work through an agency, you need to be aware of the HMRC process called IR35 (Google it). This makes it very difficult to abuse the 'rules' over employee v. self-employment as a mechanism of tax/NI avoidance/minimisation. Many agency staff have to be treated as employees of the agency because of it.