That sounds exactly the problem. I have had the same problem with Honeywell motorised diverter valves, three failed in less than 10 years. When the motor failed an internal springs closed the valve, although it could be opened manually. Check to see if there is a small lever and catch that allows you to set the valve to Open. The downside is that you can't have hot water only until the valve is replaced (not really a problem at this time of year!).
If the valve is external to the boiler get a jobbing plumber to replace it rather than a more expensive gasfitter (or is a simple DIY job, if you are up for it). If the valve is internal to the boiler you will need a Gas Safe installer to replace, even if you're not actually touching the gas pipework.
Tom, November 2009