How far are you getting through the ignition sequence?
Air pressure switch
you can here the ignition clicking as if it is having problem igniting it you give it a bag sometimes it just starts. Not sure about the sequence I presume it at the ignition stage.
If you give the boiler door a bang not bag, sorry
Ok, that is a lot of things that are still ok then.
Perhaps a poor spark or a sticking gas valve?
When was the last time it was serviced?
Perhaps worth spending £50 on a service as they can check the voltage to the pilot coil at the same time
You cannot get the coils any more so it would be a gas valve swap