Off-screen though, it was a different story altogether. While Morse was played by John Thaw, who grew up in the tough Longsight area of Manchester, Whately was the grandson of the Rev Herbert Whately, the Oxford-educated former rector of Church Stretton.
"There is an inscription to Herbert Whately in St Laurence's Church," says present rector, the Reverend Richard Hill.
Established: 12th century
Main services: Sunday 8am, 9.30am (formal) and 11.05am (contemporary)
There is a ceiling sculpture depicting St Laurence and his martyrdom on a gridiron, which was dedicated to twins Alistair and Jonathan Goulder, aged seven, and their nine-year-old brother Korwin, who were killed in a fire at The Hotel in Church Stretton in 1968
In the churchyard are 13 listed structures, each of which is designated at Grade II. They include the north and west walls, stiles and gates
To the south of the south transept is a sundial, which originated as a medieval churchyard cross, whose shaft is sunk into a former mill wheel
"I believe Kevin Whately's aunt had been seen in the congregation of the church in the recent past."
While there has not quite been an deluge of Inspector Morse fans beating a path to the door of St Laurence's, there are no shortage of visitors.
"The visitors' book has become so full, we had to take it away and put another one in," he said.
"The church is open throughout the day, and there aren't many times when there is not somebody having a look around. We get people who have got relatives in the village, people who are here on holiday, and we get visitors from places like Australia and Canada. One Australian visitor wrote upside down in the visitors' book."
This week, the church has been even busier than usual, hosting several concerts for the Church Stretton Arts Festival, and Mr Hill says the church is the focal point for many activities in the community.
"The church is the biggest building in the village, so when there is a big event in the community, St Laurence's is usually at the heart of it."
Mr Hill, who has been in the parish since 2008, says one of the most common comments about the church is how well it has successfully blended new features with the old.
There was initially a little resistance when the wooden pews were replaced by modern chairs he says, but adds that most people recognise that the new seating is not only more comfortable, but also brings out the historic architecture of the church.
Indeed, it might be pointed out that the story of St Laurence's has been one of evolution through the centuries, with the original Norman nave being extended in the 12th century with the addition of two new transepts.
Extensions to the transepts were then added by renowned Shrewsbury architect Samuel Pountney Smith from 1866 to 1868, and the north extension is now enclosed by a glass partition to form an Emmaus chapel.
Another interesting feature is a window dedicated to Wellington-born children's author Sarah Smith, who used the pen name Hesba Stretton. Her adopted first name was a combination of the initials of her and her brothers and sisters, with the surname coming from the nearby village of All Stretton where her sister Anne owned a house.
Stretton's children's novels, with a moral tale, sold in huge numbers during the 19th century.
For a church in a small village, St Laurence's has a healthy congregation of around 70, although it can get very busy during major events, such as the services at Easter and Christmas.
"The biggest event is always Remembrance Day, we will fill the church, and also have another 120 over at the parish hall for a more informal service," says Mr Hill.
He says the church also has a very close relationship with St Lawrence's CE Primary School, and hosts its leavers' services and Christmas carol concerts.
And just as the church has successfully blended the old and the new over its 900-year history, Mr Hill says one of the things which makes St Laurence's special is the way that it offers something for all tastes, be it those who like the traditional services to those who prefer something a little more informal.