My experience as a Home Visitor for Age UK was that the biggest cause of loneliness in old age is disability. For many people, particularly in rural areas, and I include my parents-in-law in this group, social life was on the street, you met neighbours and friends as you walked to and from the shop, at church, village social events, and on the bus. They were rarely invited indoors, that was family only.
Once you were house-bound your social life was gone, because social contacts were never invited into the house, so never called either. Most I met had supportive families, but unless they lived close they only saw them at weekends. Other problems arose when the older person did not admit to themselves, let alone anyone else just what problems they have. I once had to abort an Attendance Allowance application because the applicant told me about the problems she had but when I wrote them down and read them back to her, which I was obliged to do, promptly denied everything she said and claimed I had made it up!
We also must remember that some elderly people in their prime were not nice people, were not good parents and to a certain extent brought their problems on themselves. One elderly man, weeping for his wonderful wife and unvisited by his children I learned later terrorised his wife and children with his violence and had recently been banned from local pubs for threatening people with his walking stick. It is not surprising he was alone and unvisited.