so you know what we suspect:
it is very common for the water supply that tops-up the system to fail, especially in a system which is open-vented and/or old and/or neglected. If the amount of water remaining is insufficient to circulate, some or all of the radiators may be cold, and the hot water cylinder may be cold Fault will be worse at the highest point). The boiler will not fire for long because it will overheat the small amount of remaining water very quickly.
Sometimes this is because the Feed & Expansion tank is dry because the float valve is jammed, more often it is because the system is old and dirty, and the supply pipe is blocked with sediment.
The system can continue to work with the water already present, and the problem usually manifests itself when it will not refill after a radiator has been taken off for maintenance or redecorating, or after it has been partially or fully drained.
Your circumstances sound very much like that, but similar symptoms also occur for other reasons, for example poor circulation due to a pump problem or an air lock or a sediment blockage or a faulty valve.
I would like you to see if water squirts forcefully out of the highest radiator in the house when you bleed it, the reason is that this test displays if there is a shortage of water in the system (which we suspect). This is also a very easy and quick test to perform which does not even require the use of a spanner or a step-ladder and can be done in a couple of minutes.
If there is a shortage of water, then looking in the F&E tank will tell us if it is due to a jammed float valve. If not is is very likely the sediment blockage.
However, if you do not have a shortage of water, then we will be looking for a different cause.
Knowing the cause will help identify the cure.
