Nebula

Westminster can overrule the very existence of Scotland and Wales as anything other than an idea in people’s heads. Canberra cannot do that. It’s not even remotely similar.

I think Westminster can't stop Scotland and Wales existing as physical realities any more than Canberra can. Trying to snuff either of them out as political entities would now probably provoke a constitutional crisis. It's not the 1700s any more.

As it is today, the UK operates under the idea that the “British” are a single unified nation

Yeah, no. Most of the people who pretend that British means any unified thing are in a few right-wing parties.

In a London or Sydney–based game, I would probably use the city councils as the 3nd administrative division and suburbs for 4th, but maybe someone with more knowledge could address it better.

I wouldn't in London. The only city council is Westminster, so it would leave big gaps in the map. The City of London has a Corporation rather than a city council as such. You'd probably want cities/boroughs (1st-level) that contain parliamentary constituencies (2nd-level) that contain districts/liberties/communities/parishes (3rd-level) that contain wards (4th-level) but even that is imperfect and probably subject to variation in some area or other.