Had a chat with a local FISO here in UK.
Booking out over the radio fine with him when he's quite and this is normal for aircraft based there. Visiting aircraft (PPR) pilots toddle up to the tower to pay their landing fee and tend to book out informally when they do so.
He would normally like the intended destination (or that it is a local flight) and number of POB. The fuel endurance and type gathered by the phone-based booking out procedure of another local aerodrome is irrelevant to him and felt to be the pilot's responsibility. During our approx. 15 min chat on a fine day, there was one radio call.
Potentially opening another can of worms, he also pointed out that the airfield's website publishes live information that is similar in content to a typical departure ATIS announcement, thus making the initial call shorter than it might otherwise be.