[opless]

Yes, and to be paid via PAYE you need a NI number.

The prove right to work is a slightly newer thing thats additional

[mnahkies]

The nuance is that you can have a NI number, then have your visa lapse for whatever reason - you still have the NI number. Hence the requirement to prove your right to work through another means.

Previously you could use proof of British nationality or a physical biometric residence card - but they've been replaced by the digital share code system (which tbh hasn't been too bad)

[IanCal]

No, those are still the ways of proving you have the right to work, it’s only if you’re not a national that you need the share code.