The green light in the control switch is powered via a little 12v tranformer from the mains 240v supply to the heater, this suggests some mains voltage is getting to the heater, albeit little is needed to power the light.
I wonder can you hear the clicking of relays coming from behind the fire when you change wattage settings? if you can then power is definatly getting to the heater and suggests one of the two safety thermostats has tripped or failed.
One of the stats requires you to switch off the mains supply for 10 minutes before it can reset, try that first then if you have not already done so.
They do though fail and this requires replacement, not easy because the gas fire needs to come out to get at them and probably a job best left to professionals
Beyond that, the mains isolation switch is known to fail, the fuse holders don't seem able to cope with the current? this may well allow enough voltage to run the light, even the relays?, but there is not enough to heat the elements.
Not the fuse itself then but it's holder within the switch, and the whole isolation switch needs replacing.