WHAT do you think setting the hive to Gravity HW actually means ? what do you think it does, The OP has asked for a solution, I gave him the simple solution
Gravity or thermo syphon means the water to the storage tanks heat exchanger if fitted is not pumped, it does not even have to have a heat exchanger, the solid fuel cooker in mothers house did not, the water in the tap and water in the boiler were the same, and it would some times actually boil the water.
As time went on they got rid of solid fuel and at that point a hot coil was fitted, this resulted in the central heating water and domestic hot water being kept separate, however still an open header tank in loft, so hot water not potable. There was also no control of the temperature of the domestic hot water independent of the central heating circulation water, at that time central heating was to give a back ground heat only, still had fires in every room, so central heating came on morning and evening timed only, no thermostats fitted.
By fitting a thermostat to the tank during the summer the boiler could be used for domestic hot water and left on, rather than using simple timed burns, so a thermostat was often added to the tank, also people started fitting thermostats in the house, and using central heating all day long, the next major change was to add a motorised valve to the supply to the DHW hot coil.
The motorised valve allowed one to turn off the DHW heating but continue using central heating, and so one could have cooler DHW.
All these systems were classed as gravity or thermo syphon, there is not simply one C plan but 4 or 5 variations on the C plan with tweaks as time went on.
With the old gas boiler it did not seem to mind being switched off without a cool down period, however the oil boiler retained more heat, so fitting a motorised valve to the gravity or thermo syphon supply could damage the boiler, so oil boilers were not upgraded to the same extent as gas, and many oil boilers have not got a thermostat on the hot water tank, or motorised valves.
After your post I again looked on the net for information about Hive, and if there is an internal setting to switch on DHW with CH, however the instructions simple say
Hive works with most oil boilers and, if you have an existing conventional thermostat or programmer, it can replace either. If you have existing intelligent oil boiler heating controls that modulate your heating, Hive will not replace this functionality. As for installation, our engineers don’t install Hive Active Heating on oil boilers, so we recommend contacting an OFTEC-qualified engineer for help.
I have hunted for a Hive C Plan to see if there is a cylinder thermostat or not, I simply can't find one, as I have said it may work, the DHW may be turned on with CH when set correctly, but there is no official document I can find to say it can be set that way, clearly one can add a relay, so can't actually say Hive will not work even if DHW is not turned on with CH, but it would not be as straight forward to wire up.
There is a long list of boilers mainly Bosch which Hive will not work with, OK Bosch seem to want to force users to use only their systems, specially using the ebus, but main point is Hive is linked to British gas, so if some one has a problem with a gas boiler they can get some one out to fix it, but if they have a problem with an oil boiler, they are looking for an OFTEC-qualified engineer who knows Hive, not so easy to find.
So the question is simple are you 100% sure that Hive when set to gravity will turn on DHW when it calls for CH? Nest I am sure does not, as I have Nest installed, but Nest does not need to as you can wire as I have shown, if you are 100% sure I would agree fit Hive, it's cheaper and has TRV heads that works with it, but if not 100% sure, then safe bet is fit Nest which I know will work.