I have written before on why we do not need hypothecated taxes to fund the NHS.
A slightly theoretical version of the argument is here.
A more accessible one, addressing why national insurance should not be raised to fund the NHS, is here.
The essence of the argument is threefold.
First, spending comes before taxation, and not the other way round. To, therefore, ask where the tax comes from before doing more spending is to ask the wrong question as to funding.
Second, spending creates the capacity to pay more tax. The reasons should be obvious and yet apparently they are not. New government spending is, of course, someone's income. It is not poured into a black hole to be lost forever more. That means that some comes straight back in tax. And yet more comes back because the recipient of the extra income also spends, and so tax is paid, and so on. It is quite likely that over time new spending pays for itself.
Third, to link an income stream to a spending commitment is dangerous. That’s because in that case the ability to spend is artificially constrained by what happens to that income stream. However, it’s rare that there is any relationship between the demand for health spending and the economic activity that results in tax paid. The danger is, then, rationing by the back door, which many on the right would love.
Hypothecation is bad in principle. It's especially dangerous for the NHS where the ability to treat people should not be artificially constrained by bad economics.
It really is time that this idea was seen as economic nonsense designed to undermine the NHS, because that is what it is.