The problem was a faulty automatic air vent. This is a device that lets air out of the pressurised system - it was also letting a trickle of water out.
I let the boiler dry out fully, replaced the vent myself using a part from screwfix. I think it was...
Hi, I was woken up this morning by my wife complaining of no hot water.
The boiler pressure gauge was reading 0. I opened the valve and topped up the pressure, but the boiler isn't sparking. The reset button is not up. I think the fan is going (the boiler's certainly making noise)...