Yes, but why?
Just supply the rads directly from a condensing boiler with weather comp, and keep it all understandable, controllable, effective, economical, and above all - SIMPLE!
"understandable, controllable, effective, economical, and above all - SIMPLE!" that exactly describes my setup once I've got rid of the combi and replaced it with a heat-only boiler.
understandable - yup. If you can understand a combi then you can understand this setup. If you can't understand a simple thermal store then ...
controllable - yup. How controllable do you want it ? TRV sets the temperature in each room, fully modulating pump controls flow rate to match demand. No compromises to deal with minimum flow rate sin boilers and all that crap.
effective - it works very nicely thank you.
economical - standing losses for the store were measured at around 80W average. Standing "losses" for the RD532 in the house when in "keep firing up to give some semblance of DHW on demand" mode were measured at about 160W. The 80W was measured on electric using the immersion heater, the 160W was measured on gas - so allowing for a gas-heat conversion, the combi still has considerably higher losses*. Even if I were to get the newest and best combi instead of the store, I still doubt it could be both big enough to provide decent DHW and still modulate low enough for heating (and remain economical when doing so).
simple - yup. Less moving parts than a combi, easier to diagnose than a broken down combi, etc, etc.
But you missed off one key feature -
reliable. Whenever I've mentioned the number of breakdowns I've had with boilers (my parents Ideal has now broken down more than once every 2 years average, the Vokera in the flat has a similar track record), comments come back along the lines of "think yourself lucky" ! Given that condensing boilers, and especially combi condensing boilers, are expected to break down regularly then I'll take the store with it's backup immersion heater thank you very much. Have you any idea how a tenant moans when she's got no hot water or heating for 10 days ? At least at home we have an "old fashioned" OV cylinder with immersion heater for hot water, and a gas fire in the living room for heat.
* Yes, I know it's only one data set, and only one not very new boiler - but that's the data I have.