Nest heating system, hot water not firing up

Hello everyone.

We got a nest thermostat fitted a few years ago, and it's always worked perfect up until now. Lately though the water isn't heating up (for showers etc) using the app/manually using the thermostat, however if I set the home heating to come on the gas boiler fires up.

My very limited research pointed me up towards the hot press, found the two different boxes with switches on them, one clicks (the radiator one) when activated, the other one does not. I was speaking with a guy who knows a bit about these and he told me there's a manual switch/lever on these boxes, and if I push the lever to one side the water heating should activate, however it would not come off again, until I go back up and switch it the opposite way again, however moving the lever does nothing, meaning the gas boiler doesn't fire up doing this either.

I have had to start using my immersion heater for water since this started happening a few weeks ago.

So my question would be, do I call out a plumber, an electrician, or someone who installs the nest thermostat systems?

Any help and advice really appreciated.