A Roman Catholic priest tried to offer the last rites to Sir David Amess but was turned away by police because the area was a crime scene.
Father Jeffrey Woolnough said it would have been a "great disappointment" for Sir David, a devout Catholic, not to have received the prayers in person.
A local parish priest, Father Woolnough described how he arrived at Belfairs Methodist Church in Leigh-on-Sea, Essex, in the aftermath of the fatal stabbing, showing officers his identification. He had to resort to reciting prayers for at least half an hour from the road outside the church.
Not allowed on the crime scene
He told The Telegraph: "I said I was the local Catholic priest and showed them my card but I wasn't allowed. They said no one was allowed on the crime scene.
"Now we know more about what happened I can perhaps understand it, but it's still a great disappointment for any Roman Catholic - they want to receive the last rights."
Father Woolnough, who held a vigil in memory of Sir David yesterday, added: "I always use the analogy of priests working on the battlefields in the world wars. They were anointing the men as they were dying.
"We need to be a bit more brave, I think, have more courage, because that's what we're here for."
According to Catholic teaching, the last rites is a sacrament which cannot be performed after death.
Sir David was a stalwart of the local Catholic community, regularly visiting the various churches in the Southend area.
Another priest, Father Alex Poblador, described the veteran Conservative MP as an "inspiration to us all" and "a local saint".
Importance of religion for victims of crime
Essex Police last night said preserving the integrity of crime scenes was of "the utmost importance". A spokesman said a secure cordon was a "fundamental part of any investigation to ensure the best possible chance of securing justice for any victim and their family".
However, Father Woolnough made a wider criticism of contemporary police attitudes towards the importance of religion for victims of crime.
"If you're a Catholic, it's really important that if you're involved in an accident you have a card saying 'I need to see a priest'."
He added: "The police don't call you anymore unless the family ask for it. You can't give the last rites when the person is dead - it's the last sacramental right that Christians will have before they die."
No guidance on such situations
The College of Policing, which oversees some police training and development, said there was no national guidance on granting access to priests in situations such as Friday's attack.
A spokesman said: "Officers would be expected to use their professional judgement to make decisions based on the circumstances they are faced with, using the National Decision Model to guide their decision making."
He added: "Officers also have a responsibility to secure evidence and preserve any and all crime scenes."