In larger airports with parallel approaches or multiple runways, i usually check in with 'Airport Tower, Callsign 123, 26L' (so specifying the runway to give an opportunity for them to tell me i've cocked it and found the wrong runway!).
At smaller airports I occasionally add the distance to run as it might be useful to somebody taxying towards the runway (perhaps they can adjust their speed - either slow down or rush to the hold point).
At my base, on handover from approach to tower, the controllers ask us to call them with callsign only, 'Airport Tower, Callsign 123'.
No idea what the CAP413 says or the Gen, but I find that at least in my very large airline, this is pretty standard practice.