Does the heating and hot water in your house just come from the one combi boiler ? If so, then that's a pretty simple system with a simple type of wired thermostat, so I would expect switching over to a smart thermostat to be fairly straight forward. If the house is split into different zones (any other thermostats ?) or you have any additional hot water storage, then things could get a bit more complicated.
Which smart thermostat were you thinking of ? I replaced the thermostat on my Worcester Bosch combi boiler with a Google Nest thermostat without any issues. Having had it for over 4 years now, there's no way I could go back to a non-smart system !
I'm not sure how other smart thermostats are set up but, in the case of the Nest thermostat, it isn't quite as simple as swapping the old thermostat for the new one however, as the thermostat itself is wireless and there's an additional bit of hardware called a 'Heatlink' that sits in the system in-between and communicates with both the thermostat and boiler.
It may be that some of the other smart thermostats do allow a direct replacement of the old thermostat with the new one, so that might be something to consider if you want the simplest installation. You'd have to look into this though, as I'm not familiar with other systems - I'm fully into the Google 'eco-system' so the Nest made the most sense for me and it is often reviewed as the best option.
If you are interested in the Nest thermostat, then let me know and I can explain a bit more about how it works.