A bit hard to see bulb in the image, but it looks like a G9 Halogen bulb.

Just grab the bulb and pull with a little bit of a wiggle, and see if it comes out.

https://www.bunnings.co.nz/philips-halogen-capsule-g9-60w-frosted-2pk_p00244828

A slight concern I have is that on one fitting, the glass came free really easily (though I can't see how I am going to get it level again), but the identical fitting, the glass seems very resistant.

Looks like a G9

Normally on that style of fitting the center ring will turn slightly and unlock the whole piece.

I say usually because there's an insane amount of downlights like that and they all differ....

I think you are right, thanks. I'll confirm tonight.

We have two, and next time we have a sparky in, I'll do it, but I am not going to pay a callout for that one job if I can help it.

Pretty sure I have some g9 leds in the drawer. I'll see how it goes. cheers

The white surround should rotate/unscrew and drop out. They're aluminium and prone to light corrosion so it might not turn smoothly. As others have said it looks like a G9 bulb that should just pull down and out. Again these like to get a bit stuck so it might need a wiggle. 

I agree that the G9 retrofit bulbs from ebay are terrible light quality. I put six into my bathroom mirror lights, but I've taken three out and replaced them with standard bulbs. 

If bulbs are used many hours a day LED is worthwhile, but even if they're used an hour a day the cost of power for bulbs in task lighting isn't that high.