The Church of England’s automatic right to appoint 26 bishops to the House of Lords should be repealed, a report by a group representing more than 100 parliamentarians will recommend this week.

An all-party caucus of humanist MPs and peers says reform of the way parliament works must include removing the guarantee of seats in the upper house for Anglican bishops.

The All-Party Parliamentary Humanist Group (APPHG), comprised of 115 MPs and members of the Lords, point out that the only other country where senior clerics must have seats in a parliament is Iran.

The APPHG report will be published on Tuesday.

Their report highlights how parliamentarians who don’t take part in Christian prayer services in the Palace of Westminster are discriminated against.

Humanist, atheist and secular MPs can miss out on seats in the House of Commons green benches for PMQs and other key debates, the report argues. It states that “prayer cards” for those taking part in services can secure seats.

The report also calls for the introduction of “humanist pastoral carers” who can meet the pastoral needs of the growing number of parliamentarians who are humanists, atheists or agnostics at Westminster. It stresses that in other places, such as hospitals and prisons, non-religious humanist pastoral care services are provided.

On their recommendation about Church of England bishops, the report cites nine cases where senior Anglican clerics used their guaranteed seats in the House of Lords to change the outcome of votes.

These include two that directly benefited the C of E, the report says. In the first bishops’ votes helped remove a clause in the Equality Act 2010, which enabled the C of E to have wider exemptions in its employment practices.

The other vote on the Education and Adoption Act 2016 ensured that C of E maintained schools that are failing can be forcibly converted to academies, which the report says gave the church more control over its schools.

The report criticises the unique speaking rights afforded to Anglican bishops and access to officials who are charged with writing new laws.

On the issue of prayers before crucial Commons votes, one MP in the report said: “I stand outside the House of Commons chamber at the start of the session, peering through the window as colleagues take part in prayers. Whilst I appreciate it means a lot to them, the rituals make me feel excluded. I’m unable to take part in the start of the parliamentary day unless I lie and profess to believe in something I do not.”

The report recommends replacing prayers with a daily “time for reflection” similar to that held in the Scottish parliament, which would be “inclusive of the broad range of religious and non-religious worldviews in today’s UK”.

Conservative MP Crispin Blunt who chairs the APPHG said: “The UK is more diverse than ever before and yet our parliament remains an institution that marginalises those who are not Anglican. This report highlights the dated nature of our system where non-Anglican MPs and peers like me can be put at a disadvantage because they don’t wish to attend prayers.

“It is now time for us to consider how prayers as part of our procedures could be replaced, perhaps with an inclusive time for reflection, ensuring all parliamentarians get the same rights so that everyone can take part in the day’s business without having to compromise values important to them.”

The parliamentary group is backed by Humanists UK. Its chief executive, Andrew Copson, said the end of guaranteed seats for bishops, secular alternatives to prayers for non-believers and humanist pastoral care in parliament was part of the equality agenda at Westminster.

“When you have been privileged for so long, equality can seem like a step down, but I hope that Anglicans, in particular, will be able to see that the authors of this report are aiming for a broad and inclusive approach. This report shows the way forward to a parliament that treats its members equally, regardless of religion or belief and – just as importantly – is more reflective of the diverse public it serves,” Copson said.