I've seen it posted on the forum that ECNs can only be used in off-street car parks, and what I have managed to find from google seems to support this too.

But in the last few days I have seen ECNs issued to parked cars:

1) In on-street pay and display bays, and
2) In free on-street bays with a time restriction.

Is either of these allowed?

yes

under the 1984 statute the local authority obtains an SI
and can enforce ECNs under this

unlike a TRO/TMO the SI cannot be amended by the council
but only by the minister so the are often out of date

exactly what and how they enforce will be in the local SI