A general rule of thumb:
For a brand new installation - it's an electrician's job.
For maintenance and replacement of plant ie valves, pumps, immersion heaters, cylinders, its a plumber's / heating engineer's job
For fault finding, if something's not working as it should, your best bet is to use an electrician to narrow the problem down, then a plumber to change the part (if its part of the plant), if required.
Hot water and heating controls are generally a bit of a grey area between the two distinctive disciplines and requires a tradesman who specialises in one, but has good experience in the other, to carry out these works.
While we do know our way around a heating system, and can certainly help with the electrical controls such as wiring pumps, thermostats, wiring centres, etc, we leave the wet part to the experts. If you need a local & reliable plumbing and heating firm, we openly send our clients to Southway Plumbing and Heating, who we've worked with on many projects in the past, based in West Malling, Maidstone