Hopefully i can help..
Provided you have check all the obvious first then the next step will be the switch - There should be a switch "reverse light switch" on the gearbox - on top of the gearbox near the rear of the gearbox housing i recall..it has a two pin plug connected to it - once you've located it then disconnect the plug from the switch and bridge the pins in the plug either with paperclip or small section of wire - not on the switch itself on the box / switch ignition on and then see if the reverse lights are on..if so then the switch needs replaced - you should be able to aquire a reverse light switch from pretty much any good local motorfactors..quite cheaply..depending on the gearbox you have - the switch will either located as mentioned above you will need an open end or ring spanner to undo the switch and reinstall the new one - then when refitted - fit the plug connector back on and re-test..I do hope this helps..if you need to ask anything else or include further info then just continue before you rate
The switch should look like this below as an example..
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Thanks Robert, i will have to get it into the garage as i cannot access the gearbox