Hi Z,
As you have already discovered there are a variety of ways to notify an aerodrome that you want to go flying (book out).
You might wonder why we have to book out. Talking to the airfield operator, atc, flight information centre or air/ground communication service means that you will, at least in part, be complying with Rule 11 Flight within aerodrome traffic zones and/or Rule 12 Movement of aircraft on uncontrolled aerodromes of the Rules of the Air Regulations 2015. (Which can be found in Section 2 of CAP 393.)
If I am departing from a unfamiliar airfield then in the absence of an easy to find booking out instruction I just phone the ATC or Operations number in the aerodromes AD entry in the eAIS Package UK, or Pooleys or AFE flight guide. Same if I’m booking in. Also it is often much quicker to use the phone than some of the aerodrome website PPR forms. On many occasions it has been a phone call or text to the mobile number of the aerodrome operator. Most recently, for example, the charming and helpful Peter Robinson at Sutton Meadows.
Anyway, I wouldn’t worry too much about the method as long as you have obtained the permission and information that you must have to comply with Rules 11 or 12.
JP