Probably just got dust in the hazard switch, work it up and down really fast a few times usually cures it. Blow it out with compressed air.

Reverse lights aren't part of MOT but you need to see if any power and earth at the bulb holder, check the fuses. Also on the front of the gearbox you have the reverse switch, disconnect it and get a paper clip, with the ignition on, put the paper clip in the connector to bridge the terminals, the reverse lights should come on, if they do, it's the switch fault.

Don't let the paper clip touch any metal parts of the car when testing it, as will blow the fuse