NUTS is yet another way of dividing countries into smaller subdivisions. It's been renamed to ITL since Brexit, although the defined areas currently remain the same.

I've added level 2 and level 3 data to the main postcode CSV downloads (NUTS level 1 data was already available as the Region column). If you'd like it available in any other formats, let me know.

UK Postcodes (doogal.co.uk)