Dave has hit on just what I was going to say ^^^^
It does sound as though your circulating pump is either faulty or stuck.
When the thermostat /timer clicks on, it calls for the boiler pump to start up. It sounds like this isn't happening.
If it's a combi boiler, the pump may not be so easy to get at, but if it's a conventional boiler, then the pump will either be near the boiler, or in the airing cupboard.
There are Youtube videos I've seen, that show you how to free up a stuck pump.
Search in youtube for "freeing a stuck circulating pump"