Thank you so much for bothering to help (unlike some).Getting to my limits of usefulness I'm afraid
It sounds to me that the valve has got stuck with the micro switches in the on position. Not sure how that works when you say both sliders on the timer are switched to the off position!!!
Not sure if there is any way to free the gears/working of the valve. What ever way of doing that you would have to be careful of live electrics etc.
Perhaps that would become apparent when/if you take it off. Freeing the valve may resolve the function of the three way valve, solving the problem!
However requesting a plumber to call with the hope of now sounding a bit more confident regarding three way valves is somewhere near to saving you a bit of money.
I think my logic is just to get a new silver box for the valve and fit it (freeing up the vlave itself whilst the box is off) - I don't think they're massively expensive?
From what I can see on Ebay, a three port valve with motor etc is about £30 for a new Honeywell unit. I'd be buying the exact same make/model so that I can turn the electric off and simply pop the old silver box off, put the new one on, wire it in and hopefully problem sorted?