You do not say the boiler make & model...
On many boilers the pilot does go out when the main burner goes out & relights when a new call for heat arrives - if the pilot in your mum's boiler lights on its own and goes off on its own there is very probably no issue with the pilot.
The boiler firing for C/H is controlled by the timer programmer and above all by the room thermostat that sets the required air temperature.
Most boilers have a user control on the boiler itself to set the temperature the water is heated to - usually they get set to the mid mosition - the boiler thermostat.
Radiators may need to be bled of excess air with a radiator key. If a radiator has a TRV control the control pin sometimes gets stuck in the off position - an easy fix.
The pump that moves the water around the system can sometimes be adjusted to pump faster - to get the water around the system before all the heat is lost.
Try running the system with all the radiators turned off except one and see what happens to it.
Good luck...
Peccavi
January 2010