And back to the orginal topic - do both Jason & Alex have full talkback or just part talkback (i.e Gallery presses a button to talk to them -forgot what it's called).
"Keyed talkback"
It's pretty unusual for presenters to have full* talkback, as there is so much other stuff going on, as Jake says in his blog, it's something which he learned and is used to it, but I know other presenters who get upset if they hear stuff not aimed directly at them, especially while talking on air.
It's usually known at the BBC as "Switched Talkback" with the other version known as "Open Talkback" (rather than "full").
Sport and News presenters, as well as presenters on busy live kids shows are usually used to "Open", whereas presenters on pre-recorded shows, those with much longer-form interviews (Newsnight, The Andrew Marr Show etc.) and that are more rehearsed and less likely to change are on "Switched". "Switched" is common on entertainment shows, and in some cases presenters on these types of shows aren't on talkback at all, and are guided entirely by the floor manager. (Wogan famously worked this way on his BBC chatshow, and had idiot boards rather than on-camera prompt)
Which type of talkback the presenters on The One Show are on is a decision the presenters and director will take together, and may not be the same throughout the show, or may differ during rehearsal and transmission.
In some areas, it is common for presenters to move from Switched to Open, so that they can concentrate on interviews without hearing lots of other stuff, or if the interview is over the phone, concentrate on working out precisely what is said.