Will a kitchen fitter do the tiling and the gas/electric installation etc

If the kitchen fitter is competent in all trades involved and able to certificate the gas and electrics if needed then yes. If they are a carpenter and only do the woodwork side of the job then they may have sub contractors they use for the other aspects of the overall work.

Its unlikely that the one person would be able to do all of the work correctly and legally.As stated already,gas and electrical work has to be by someone qualified to do so.If your fitter arranges or carries out this work,then make sure it is by someone registered with the appropriate schemes ie nic and gas safe.