Well it's apology time...
John tbm... this link supports what you say about the mid position valve sending turn-on power to the boiler...
http://www.diyfaq.org.uk/plumbing/controls/controls.html
It seems that because of the slightly strange wiring of these control valves, when the programmer and thermostats are requiring Heating Only the mid position valve is organised to make the call for heat else the boiler won't fire - I never knew that!
Foston, I'm sorry - I'm unable to imagine a single boiler supplying hot water to two storage tanks and that coupled with your conflicting trouble statements (boiler never firing for water and then just firing for 20 seconds) made me suspicious of your circumstances and imagine that you're a landlord.
If the call for hot water only makes the boiler fire for just a few seconds I can only think that some kind of wiring fault is not making the circulating pump run and the overheat thermostat is shutting everything down - but I'm just guessing. You do not tell what happens next if anything - after the boiler fires for 20 seconds and then shuts down - does it try again on its own some time later?
You do have immersion heaters I suppose?
Good luck...
Peccavi
March 2009