I have heatmiser stats and quite like them. On mine the wiring is as Lectrician describes.
Live - L (and a link between L an A1)
Neutral - N
Switched Live back to the boiler - A2
See "Heatmiser PRT Standard" on page 19..
http://www.heatmiser.co.uk/manual/dt/dt_manual.pdfI've got a feeling the Honeywell stat is battery powered and will work without a neutral wire (on it's terminal 2). So although you have enough wires in the cable to provide a neutral there may not be one connected at the boiler end. Hence the new stat doesn't power up.
You would expect there to be a neutral somewhere near the boiler so probably not hard to provide one and get the heatmiser going. If you can't check that the answer might be to find another battery powered "two wire" stat that doesn't need a neutral.