You will not be able to have CH without DHW when there is no tank thermostat. Likely you are running C Plan and there were three stages of the C Plan, very old like yours and mine there is no tank thermostat and the boiler can be used for DHW only in the summer, but on a purely timed basis, I found fitting Nest means I can run the boiler for shorter time and every other day in summer, I have it as ½ hour for 3 days a week and hour for 4th to stop legionnaires. Winter no control of DHW it comes on with CH.
I had a problem in the summer with three stores in the house, the radiators would to a small extent thermosyphon, idea is pump does not run if you don't want CH, but water will pass through pump, in theory with TRV's on every radiator they would stop thermosyphon, however when I moved in some were simple liquid type, and on a cold night they would open, so rooms warmed up, when likely latter in the day we would need the AC switching on, so not ideal, now with programmable TRV heads fitted it would stop the thermosyphon but had second problem two pumps one for lowest floor which had been turned into a flat, and one for rest of house, and one pump caused the other system to work backwards. So I fitted motorised valves so central heating in summer is off.
The C plan was latter modified adding a thermostat to the DHW tank, this allows you to leave the programmer at 24/7 for DWH in summer, and it only fires up when required, the problem for me is running the cables water tank to boiler so I am still timed, there were wireless versions, but supply seems to have dried up, but on my to do list.
There was also a third modified version where a motorised valve is added to the DHW with that you can also limit DHW temperature in the winter, my plumber says I should not fit one, as it stops the boiler cooling after switch off through the DHW, not sure how true this is? But I have not fitted a motorised valve to DHW as a result of his advice.
Hive and Nest are wired different with C Plan, I am told setting Hive to gravity the DHW relay works the boiler, and the CH relay works the pump, and Hive automatically switches on both relays with CH and only the boiler relay with DHW, but with Nest you have access to the com terminal of the relay, so com goes to boiler and N/O is always line, and N/C goes to CH N/O doing the same as Hive but with wires not software. As soon as a tank thermostat is added then the N/O and N/C contacts of the tank thermostat are wired as with Nest instead, I would guess with Hive it would not be set to gravity even though it is?
Biggest advantage with Nest (over original programmer) is being able to program shorter runs for DHW, however the hot coil will not transfer heat fast enough, so that ½ hour slot is really 20 minutes as the boiler turns off for 11 minutes as too hot, and by time it switches on again the time has lapsed. Once the boiler and pipe work are hot, (20 minutes) the boiler will cycle around 50/50 to start with slowly decreasing the run time each time is cycles, not impressed with the DHW as it takes so long for hot water to reach taps. (Originally programmer 1½ hour slot was shortest).
To me the problem with EvoHome, Tado, Nest and Hive is actually getting info on how it works. Once fitted you find out of course, but look at adverts it does not say things like minimum time between temperature changes is 1 hour, or minimum run time is ½ hour, and Nest does not publish a C Plan so as the installer you have to work it out for your self, although I now have one.
I think I would today lean towards Hive, as they have TRV heads to work with it, where Nest at the moment does not, don't know Tado, as far as I can tell EvoHome seems the best, but seems you must fit TRV heads where with Hive you can add TRV heads latter, also with gas boilers the OpenTherm is added extra with EvoHome, it is standard with Nest, and unavailable with Hive. So for gas Nest has an advantage, but with oil it does seem Hive has the advantage which makes one ask why British Gas pushes Hive, however with Worcester Bosch which BS also seems to push, there is no OpenTherm you have to use their own special system.
I note Energenie MiHome which did work with Nest until Google took over Nest, now do their own wall thermostat, since I already have Nest, I have not really looked at it, but as a complete system it is likely one of the cheapest, although the Hive wall thermostat is cheap, the TRV heads are not, although I have 4 Energenie MiHome TRV heads which when bought were suppose to work with Nest, I also have 5 eQ-3 heads, far cheaper, and they seem to work very well.