What type of stat is it? A manual one with a knob? You can usualy get some clue as to whether the they are swiching as you probably would be able to gear a click as you rotate the dial. Joe Offers method is more reliable though - s simple continuity test.
You could well find you have a faulty unit but I believe Honewell are OK. I've a feeling they are American but thier heating controls are widely used in the UK.
Don't know what other makes you might get. Our own is one of these Danfoss-Randall ones. Works fine. I fitted the controls a year or more back as there was no room stat, no cylider stat, and no zone valve for the hot water side of the circuit, going radio conroled to avoid wiring tasks I didn't fancy. We have made significant savings in oil consumption since moving from the system that was just controlled by timer to this.