A funeral was delayed for two hours because of a dispute about the size of the grave.
Peter Worby said his father William was due to be buried, but a priest at Old Hall Green in Hertfordshire said the grave was not deep enough.
After an agreement was reached, the priest allowed the 98-year-old’s burial to go ahead, but Mr Worby said his family were “robbed of grief”.
A senior Catholic bishop apologised for “the added distress”.
The dispute arose in the lead up to Wednesday’s service, but Mr Worby said the family believed it had been resolved in advance.
Mr Worby, 62, said he arrived at the Church of St Edmund and the English Martyrs on the day of the funeral, could not find the priest and was informed he was at the burial plot but there was a “problem” and the dispute was continuing.
“I got on my hands and knees and measured the grave which was 46in (117cm),” said Mr Worby.
“In sandy soil the minimum recommended is 24in (61cm) and when my father’s coffin went in it measured 30in (76cm).”
According to the Natural Death Society, there is no legal minimum depth for a burial but the Ministry of Justice recommends a minimum of 24in (61cm) of soil between the coffin lid and ground level.
After more discussions, the service went eventually ahead.
“Many mourners had to wait outside in freezing cold as only a few could wait in the church hall due to social distancing,” Mr Worby said.
“I begged the priest to allow my father to be buried. I was in disbelief. I feel robbed of my grief.
“My family and I all agree, it wasn’t a funeral. We were all in shock and anger.”
In a statement, Bishop Paul McAleenan, Auxiliary Bishop in Westminster, said: “Every effort is made to carry out this important duty with dignity for the deceased and care for the bereaved.
“Unfortunately on this occasion there were some complications involving the grave plot which upset the family of the deceased.
“We are sorry for the added distress they suffered as a result.”