Why fuel guage is not working

I'm not sure you have to have a working fuel gauge for the MOT.

No issues with the fuel guage that I know of , but you can follow the basic troubleshooting guidelines. Starting with the wiring disconnect at the fuel tank for a bad connector or bad connection. Only other connection would be up to the instrument cluster in the vehicle. Only replaceable items would be the guage or the sending unit in the fuel tank. You can disconnect the return line circuit or connector at the at the gas tank and jump a wire to the ground the that feeds the gauge and see if the guage moves, but don't and i repeat don't hold to long because the guage will go over hard over and could damage the guage. If the guage moved and I would suspect a bad float on the sending unit or a bad sending unit, either case the fuel pump assy would have to come out for repairs.

temperature sender unit top of engine cylinder head make sure its okay
and make sure wire going to it is not grounding
if it grounds or earths it will send the gauge up and down

there are 2 relays inbetween the fans they are known for the wiring corroding and causing problems with the relays
get this checked and replace the relays and conectors if needs be

ensure that your power steering oil is at the right guage

sounds like the fuel gage in the tank is not working and need replace

sound like you knock a wire loose from the guage. check your wiring. Sound like the ground wire is off, or loose.

put the car on an oscilloscope and check what is happening,check cranksensor,injectors,fuel pump supply,coil packs you will then see what you are loosing if its power(electrical)or a fuel problem put a fuel pressure gauge on it and road test it you will then see whats happening.........oscilloscopes dont tell lies.....

drop fuel tank. if guage moves all around its probably the fuel level sensor on fuel pump assembly in the fuel tank. If the guage stay's in one spot its the guage , replace instrument cluster assembly. you can take just the glass off the cluster and move the fuel guage needle and it will work (if stuck) but for how long? The wires to the guage come from the sending unit to the power train control module to the instrument cluster. pray its not in the wiring.