Like you say, NHS/GIG, UK/DU, USA/UDA are all commonly used, at least as written forms — but none of them are spoken as acronyms, as far as I’m aware.
These ones are pronounced as acronyms: IT/TG (tuh-guh), GCSE/TGAU (tuh-geye), WJEC/CBAC (cuh-bac). One problem with Welsh acronyms is they tend to have lots of Cs in them. I can think of at least three institutions whose acronyms are CCC, which isn’t much use!