There's still the question of whether England, Scotland and Wales are countries. I think these are good examples of how important recognition is. In the case of Wales, there can be little doubt. It was conquered, its people served in English armies since the hundred years war and its affairs have been handled by England for centuries. There is just no legal support for Wales being a country.
The case for Scotland reinforces that of Wales. Scotland was an independent country. It accepted England in a personal union at the death of Elizabeth I, but remained a separate country. All changed with the Act of the Union, which amalgamated Scotland with England (I am leaving out Ireland here because it complicates unnecessarily), stupidly retaining the English, rather than the Scottish numbering of monarchs (this may have been a negotiating sop to the English, who were losing their independence) under the queen of Scotland. Scotland was henceforth part of a federation with England and Wales and the parts of the federation got equal status. This is no different from Swiss cantons, US states, Dutch provinces under the Republic, Malaysia or Australian states.
Importantly, the act of the Union was internationally recognized by the behaviour of other states: they explicitly or implicitly accepted the British (federal) government as representing the whole federation, not just Scotland. Therefore, there is no international recognition that England, Scotland and Wales are countries, so they are not (notwithstanding the IOC and FIFA

), just like Zürich, Texas, Holland, Selangor or Tasmania.
That doesn't mean such non-countries cannot issue coins. It does means that they need permission from the federation. Sometimes, the constitution will be in the way of sub-national coins, most of the time there will be no political will to grant permission. A compromise may be to issue coins with a nod to the constituent parts of the federation, such as "Scottish" and "English" shillings or "state quarters". Even in the case of the Netherlands, minting was decentralized, but the weight and fineness of the coins were agreed on a federal level.
Peter