Towards the beginning of this episode, Brian has to take Esther to hospital, which makes him late for work. Jack makes numerous attempts to contact him using his mobile phone. He then receives a call, and states to Sandra and Gerry that the caller is Brian, but we then see that Brian made the call on a payphone at the hospital. Jack couldn't possibly have known that it was Brian who was calling him.
Esther has injured her arm so badly she can't even move her right hand. Gerry and Brian serve her dinner in bed - with the salt and pepper on the tray in grinders of a type that are tricky to operate even with two good hands.
The team have a selection of recordings of the Campbells' TV shows to look through. Jack mentions that shows like that were all live in those days, i.e. the Sixties. However, neither the BBC nor ITV were in the habit of recording "live" shows for posterity unless they had historical or commercial value. A bog-standard cookery show, no matter how popular, certainly would not have had such value, which is why very few if any of Fanny and Johnny Cradock's shows, which presumably the Campbells' are based on, exist today.
Since syllabub generally contains some alcohol, it is unlikely that any of the team, particularly Esther, would allow Brian, as a recovering alcoholic, to eat any.