You don't describe your boiler but I assume it's the sort that has a hot water tank in an airing cupboard.
The boiler is working correctly - it fires up to heat water.
The signal to fire up the boiler for central heating comes from the timer/programmer - then via the room thermostat and then - strange as it might seem - via the three port valve - often in the airing cupboard. A small motor moves the valve to direct the heated water to the storage tank or to the radiators and sometimes to both of them. A small switch inside the vale enclosure sends the fire-up signal to the boiler.
If the valve gets stuck or the small switch fails then the boiler will not fire up for heating - this might be your problem.
The top of the valve usually has a small manual override leaver - you can operate the valve by hand - see what happens.
If your boiler is a combi then ignore all this.
You would do well to call a heating engineer but my prejudice says to avoid British Gas who tend to sell you other services.
I am not a heating engineer - I just guess - like many heating engineers do.
Good Luck..., March 2016