Purely out of curiosity, is it legal to live in the UK without ever bothering the state at all? What is the minimum of documentation required. I assume a birth certificate and they'll probably want you to go to school. We all give up part of our freedom in exchange for advantages conveyed by fitting into ready made templates, what are the limits on pure freedom?
That's probably about the minimum, and you don't actually need the birth certificate, as such. One will be generated when you're born, but you don't have to have a copy yourself. Likewise you'll have a National Insurance number, but unless you want to register with a GP, claim unemployment benefit, or something similar, you don't need that either. A driving license is useful as a proof of ID, but again, unless you need to drive a car (or other motor vehicle) you don't need one.
Once you've left school, so long as you don't want to use the NHS, travel overseas, drive a motor vehicle, claim benefits from the state, or any number of other things, you don't really need any bureaucratic documents. Of course realistically, most people do need these things from time to time.