The question is what do you want Nest to do? For old central heating systems Nest can help, and for hot air systems it is great, but the modern system is all wrapped around the condensing boiler and thermostatic radiator valves (TRV).
The TRV gradually increases or decreases flow, which in turn decrease or increases the return water temperature which in turn lowers or raises the boiler flame height to match the demand, the main point is "Gradually" there is no sudden off or on. However there is a problem as the demand drops below a set level, when the flame height can't be reduced further, so the boiler starts to cycle, and it will reach a point where all it does is heat the pipes, all the TRV's are off.
To get around this problem we have tried all sorts, including outside sensors which are there simply to switch off the boiler when no longer required.
Today we use special TRV which transmit info back to a hub and that tells the hub when to switch off the boiler, there is a cheap system using a Nest thermostat using what is called ITTT (If this then that) so eTRV's like the Energenie MiHome can tell it to switch off similar to the EvoHome but not with as many bells and whistles, since your diagram shows you already have outside sensors there is very little benefit in using a half hearted approach like Nest. By time all the eTRV's are installed you can do all the things like have the heating come on when it detects your phone is within a set distance and also manually alter with the phone.
Your picture shows the link to remove to install a remote control for the boiler, however consider first why you want Nest?
I made in hind sight an error, I fitted two MiHome eTRV's with the idea of then fitting Nest to work with them using the follow command, however when I set rooms to cool when likely not in use then heat up before required again I found there was a problem I had not considered, the whole idea is for the TRV to "Gradually" change temperature and the speed of change is built in, so when I set living room at 22°C to drop to 16°C at 9 pm over night, by 6 am when it was programmed to return to 22°C it was still only at 17°C, the same problem going up, to get to 20°C by 8.30 am I had to set to 22°C at 6 am and then down to 20°C at 8:30 am as it was built into the eTRV so as not to over shoot to re-heat slowly.
I also had a problem keeping the boiler running during the re-heat and had to do all sorts but that's another story.
So I would say from my experience either go for cheap stand alone eTRV's and keep existing thermostat, or go the whole hog and fit something like EvoHome.
I am sure in my house which is open plan with a very old boiler Nest would work, it would also work with hot air systems, but with a modern boiler and traditional house they may look good but don't expect it to control house even as well as the old wax TRV's and it will be no where near as good as a modern even stand alone eTRV as it switches on and off and the TRV and boiler are designed to gradually adjust not simply switch on and off.
