Which was one of the longest running characters in a British TV series, from 1979 to 1994, who never appears on screen?

Answer 1

Er indoors
The wife of Arthur Daley, the dodgy con man on whom the UK TV show "Minder" centres, was referred to throughout the long series as "' er indoors" and implied to be a fierce and formidable woman but never actually appears. "She who must be obeyed" was the wife of Horace Rumpole in "Rumpole of the Bailey" but she frequently appears in the series. Little Cousin Scampi was in "Sooty and Sweep", later "Sooty and Co", (1955-98) and appeared from 1991 onwards. Basil Brush presented his show.