The Christian Institute is sending a dossier about a "highly illiberal" conversion therapy ban in the Australian state of Victoria to a thousand Westminster parliamentarians.
The government's proposed ban was missing from the King's Speech at the State Opening of Parliament on Tuesday, although Cabinet Office minister Alex Burghart told the BBC that its absence does not mean it has been dropped.
"Just because something isn't in the King's Speech doesn't mean that it's been ruled out," he said.
"It's very important we get this right. What we don't want is a situation where we get legislation that accidentally criminalises parents or teachers. We do want to do something, we just don't want to end up in a bad legal space."
The Christian Institute is one of several Christian organisations to have raised serious concerns about the potential criminalisation of pastors and parents, especially as some activists are calling for "gentle non-coercive prayer" to be included in legislation.
Assurances from Equalities Minister Kemi Badenoch earlier this year to protect the ordinary work of churches and parenting have not allayed fears.
The dossier being sent by The Christian Institute to parliamentarians points to the case of the Australian state of Victoria, where a similar ban on "practices that seek to change or suppress a person's sexual orientation or gender identity" came into effect last year.
Breaking the Victorian law carries a penalty of up to ten years in prison or a maximum fine of nearly AU$10,000 (around £5,200 or $6,400).
Under official state guidance, prayers are "likely to cause harm and be a change or suppression practice" if they "ask for healing", "for a person to change", "for a person to not act on their attractions", or "talk about a person's brokenness or need to repent, ask for long-term celibacy".
To be considered harmful, the prayers must be "directed at an individual because of their sexual orientation or gender identity", or be "undertaken with the intention to change or induce that person to change or suppress their sexual orientation or gender identity".
Permissable prayers are those "that are supporting and reassuring that the person is created in their God's image and perfect the way they are".
The state of Victoria guidance also states that parents would be breaking the law for "refusing to support their child's request for medical treatment that will prevent physical changes from puberty that do not align with the child's gender identity".
The Christian Institute said there are fears that even encouraging churchgoers to say the Lord's Prayer could be regarded as a breach of the ban.
It is warning that if the Victorian ban is copied in the UK, as some campaigners want to see happen, it would result in "one of the most religiously repressive laws in centuries".
Simon Calvert, a Deputy Director at The Christian Institute, commented: "The Government has a massive problem with this legislation.
"They recognise that the terrible pseudo-therapeutic practices that were used decades ago are already illegal in the UK and any therapist claiming they can 'cure' people from being gay would be banned from practising by regulators. So what is it that is currently legal, that campaigners want to ban?
"All the leading campaigners for a ban say they want legislation similar to what was introduced in Victoria. But this is the most ideological, restrictive and punitive ban in the world.
"It even seeks to tell Christians what they can and cannot pray. Followed to its logical conclusion, guidance from the State of Victoria bans a church leader from using the Lord's Prayer with an LGBT person. Is this really what activists here want to outlaw?"
A legal opinion sought by The Christian Institute from leading human rights lawyer Jason Coppel KC has said that a new law could infringe on human rights.
Mr Calvert, concluded, "It's time for the Government to take a reality check on this virtuing signalling draft Bill. All the abusive practices you would expect to be banned are banned.
"What activists want is not a law against abuse, it is a law against disagreeing with Stonewall orthodoxy in your conversations with gay or trans people.
"As Jason Coppel KC has made clear, any legislation going further than the existing law would seriously impact free speech, religious freedom, freedom of association, and the rights of parents. It's time to ditch this legislation once and for all."