How does no one pay for it, though?
I don't know the ins and outs of the UK education system, but I have to assume the facilities and employees are still paid for.
> Does food and water? Shelter?
If everyone had access to it for free? Absolutely! I wouldn't work as a farmer or build houses if no one had to pay for those products. Value, or price in this context, is only really feasible for scarce assets. If something is seemingly unlimited and freely available it will have no (financial) value.
Tax. The missing link is those educated people pay it back with their tax. And/or contributions to the economy.
Also part of this is making education better bang for buck.
You can say who's gonna pay for it for everything. Defense and meddling in world affairs is a big cost too.
It's publicly funded, not built and staffed by slaves.