It sounds like the button is faulty, there could be some debris inside it.
Before replacing the faulty part you can try spraying some WD40 into the button (with the power switched off), while your depressing and pressing the button a few times, if this doesnt clear the fault it will need to be replaced.
As this is a Gas appliance you will need a gas safe engineer to change over the part, but this shouldnt be more than £30 labour and the part should be less than £20 from a spares place such as the one here.
Without the model number I cant provide you a link directly to the part, but if you can find it, please let me know and I can give you a link to the exact part.
Should you want me to recommend a firm to do the repair please send me your post code.
If you need anything clarified please do get in touch