I pay income tax and NI. I also have a small private pension. The NI and pension should cover the cost of my future pension if I eventually get to retire.
No, it really doesn't!
Your future draw-down dwarfs by many times over the NI you have paid, which by the way isn't and has never been a hypothecated tax. It is essentially an extra payment on income tax.
As for the income tax, I don't currently get an awful lot from it.
Roads, transport, defence, libraries, culture, arts, the emergency services, police, the civil service, scientific research, the BBC, the justice system (keeping the rule of law in your society)...and so on, and so on.... 
You never watch the BBC then? Or travel on a road? Don't expect criminals to be caught?
I rarely need the NHS and since I don't have children, I'm contributing hugely to a state school system that I don't use.
The state school system is not very expensive in terms of the overall public budget. (Compare defence, for example.)
You might not need the NHS now, but you probably will in the future. No private insurance that you can currently buy will fund what the NHS does.
The reason we have collective taxpayer-paid systems is that the costs of funding public services by individual insurance and payments would be not only astronomically large, but simply impossible to do.
If you truly don't believe in the system, why take its benefits whilst pretending that you don't? I don't believe a single person living in today's UK doesn't depend on collective provision in some way. Even the richest of Russian oligarchs comes here precisely because the tax we pay funds a working rule of law, public order and the enforcement of property rights. If you think you don't get anything much for your taxes you must have a very limited awareness of how society works!