I just noticed this clause on the lounge admittance page:
Note on First Class lounges: Passengers offered complimentary upgrades to First Class are not entitled to First Class lounge access, unless access is otherwise available based on eligible frequent flyer programme tier (for example, Marco Polo Club Diamond members will be entitled entry to First Class lounge regardless of class of travel). Customers originally booked in Business Class and upgraded to First Class will be entitled entry to the Business Class lounge.
There is a similar clause for those who have been given an upgrade to Business Class. I'm pretty sure that this wasn't specifically called out previously. I had read on here people stating this to be true, but I didn't believe it!