Places of worship will be forced to close during the lockdown unless they are being used for funerals, to broadcast acts of worship, individual prayer, formal childcare or where part of a school, essential voluntary and public services, such as blood donation or food banks or some other exempted activities such as some support groups.
Earlier this week there were calls from the chairman of Peterborough's Joint Mosque Council, Abdul Choudhuri, to keep places of worship open during the lockdown.
Today, Mr Bristow wrote to Secretary of State for Housing, Community and Local Government Robert Jenrick calling for public worship to be allowed.
In his letter, Mr Bristow said: "The freedom of our faith communities and constituents to participate in public worship is extremely important.
"The pandemic has already limited this freedom in distressing ways, particularly during the last lockdown.
"Since then places of worship have worked hard to become COVID secure environments complying with the Government's guidance.
"I know from my own visits that churches, mosques and temples in Peterborough have done everything asked of them to remain open, accepting many limitations on their activities.
"It is of deep concern to me that despite theses efforts, they will be unable to offer public worship until 2 December 2020. I know that national leaders of our faith communities have written to you, setting out why they believe the new restrictions fail to reflect this work and lack a firm grounding in scientific and medical evidence.
"They argue that many places of worship have been made from COVID transmission.
"I would be grateful if you could consider all available options to allow public worship to continue in some form. My constituents' faiths are more important to them than ever during this difficult time.
"The continuation of safe public worship must be a priority."