Both my fog lights don't work which is a pain as I'd like to see them on and I;m sure you need them working to pass an MOT? I had a go at removing passenger side wheel arch liner, I managed to have a little look with bottom screw off. I took the bulb out and it looks fine. The connectors I could see were connected so I suppose its fuse next which I understand is a pain in the arse to get to in the engine under the battery? If the fuse is ok what else could it be? Is it a common fault?
I'm not sure if the rule has changed the last few years but if they are present they have to be working to pass the MoT. If they don't work, just take them out before the MoT
If a light is present it has to be working. However front fog lights are usually not tested on an mot. If you are concerned and can't get it fixed in time just take the fog lights out before you go to your test and refit them after.
The front lights are classed as a courtesy light, so like your reverse light, it isn't tested and if it is would normally receive an advisory. The rear fog lamps however must work and are tested