The Faith in Later Life initiative, which helps churches engage with older people, made the plea as it welcomed a call by the Government's new "minister for loneliness" that more families take grandparents on holiday with them.
Director, Carl Knightly told Premier: "There are a million older people who are always or often lonely.
"We've all heard about the statistics; approximately 15 cigarettes a day [equates] to the health impact of being lonely.
"But, more than this, certainly I feel, there is so much more to gain from holidaying with grandparents than just tackling loneliness."
Mr Knightly spoke after Mims Davies said Britons could learn from how older generations in Mediterranean countries are more involved in family life.
She added: "We are in a weird place when we are very willing to drag our children around into our lives and enjoy our lives with them together - but being that sort of extended family is seen as being a bit more difficult."
Mims Davies said there was a "moral duty" for people to stop the elderly feeling neglected. She also encouraged employers to give staff more time off to look after parents.
Carl Knightly added: "It might be that somebody in a church doesn't have a grandparent and they could invite an older member of their church on a holiday to Spring Harvest or New Wine.
"It doesn't even have to be a holiday but we're really keen on this idea."
Click here to listen to Premier's Alex Williams speaking with Carl Knightly:
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