He died at the Princess Royal University Hospital in Orpington, having been transferred from a care home after developing Covid-19 symptoms.
Mr Shrosbree joined the City of London Police in 1959 and spent more than 30 years in the force. He spoke fondly of having met the Queen Mother on a royal visit to police horse stables.
A proud Cockney, he settled with his family in Chislehurst, and leaves wife Margaret, two children and four grandsons.
Mrs Shrosbree, 83, said: “He was an ideal copper, very honest and straight. He loved his job and he adored the horses. His love of animals made his job the perfect one for him. He had tested positive for coronavirus but had underlying health issues.”
Mr Shrosbree had played football for Sutton United and the RAF during his national service. After retirement he took up golf and had also helped to run junior football teams.
His wife added: “Things did tend to happen to him, once his horse did a wee in his helmet before he was called out on a job which made us laugh.”
Colleagues at the City of London force paid tribute to “a genuine, old-school friend… with a twinkle in his eye.”
His funeral was held on April 17 and neighbours saluted him as the hearse set off from the family home.