Barnaby Senior had died prior to 1996 on his birthday, whilst on a fishing trip. He and his son Tom had an argument that day and Tom regretted this for years afterwards.
He died at the same age Tom was during the events of Fit For Murder and this played on Tom's mind and was a deciding factor for Tom to retire. According to Tom, he liked Plummer's Relish.
Barnaby Senior had at least one sibling- Ned Barnaby who may have been fairly younger than him, as Ned's son John was at least twenty years younger than Tom.