Plans to introduce buffer zones around abortion clinics nationwide would be a "devastating blow to civil liberties".
Clause 9 of the Public Order Bill makes "informing", "advising", "influencing" and even "expressing opinion" in the vicinity of abortion clinics a criminal offence punishable by up to six months in prison. Repeat offenders face being jailed for up to two years.
After the legislation had its second reading in the House of Lords on Tuesday, the Alliance Defending Freedom (ADF UK) asked Christians to contact their MP about their concerns.
The advocacy group says the plans are "detrimental to society" and should be removed from the Public Order Act.
"The broad wording of the prohibition would result in a devastating blow to civil liberties," said Ryan Christopher, ADF UK director.
"Could a parent, or social worker, be criminalized for 'advising' a confused teen outside an abortion facility? Does mere peaceful presence amount to intimidation?"
Speaking against Clause 9 in the House of Lords this week, Lord Beith argued that Clause 9 is incompatible with free speech.
"When I look at Clause 9, I see understandable references to intimidation, harassment and threatening behaviour, and I am prepared to consider whether the law needs to be strengthened to prevent those things," he said.
"However, I cannot support a clause which criminalises a person who 'seeks to influence', provides information or 'expresses opinion'.
"This is the most profound restriction on free speech I have ever seen in any UK legislation, and I cannot support it if it remains in its present form.
"Indeed, I think it will be grasped as a precedent by the free-speech deniers, and the words and language will be applied in other areas when other legislation is brought forward.
"It is clearly incompatible with the European Convention on Human Rights, and the Government cannot certify the Bill in its present form for that reason.
"A lot else in the Bill appears to be incompatible with the European Convention on Human Rights, and I believe it will give rise to more litigation than improvement in effective policing."
Speaking in the same debate, Lord Farmer said that current laws were sufficient to deal with harassment or intimidation outside abortion clinics and that the "sweeping criminalisation" contained within Clause 9 was "out of all proportion" to the actions of pro-lifers.
He suggested a "cultural authoritarianism" was behind efforts to withdraw the rights of pro-life protesters.
"Furthermore, the Bill reduces the threshold of criminality to standards lower than ever before and, as currently drafted, would likely catch a parent, teacher or social worker giving, at the request of a young or vulnerable person, rounded advice to help them make one of life's most difficult decisions," he warned.
He added, "If prayer is considered a form of 'influence', then Clause 9 puts the UK's first 'thought crime' into statute."
Later on, Lord Farmer said that the introduction of buffer zones around abortion clinics could have a ripple effect, with other organisations or premises seeking the same.
"If passed into law, Clause 9 would mark the single most significant shift away from English law's presumption of individual liberty and freedom of expression in the interest of ruthlessly censoring pro-life views," he said.
"Yes, these fly in the face of our current cultural norms and may be held only by a minority, but that is exactly what our fundamental freedoms of expression are designed to protect.
"Where will this end? Banning people from public areas near abortion facilities based purely on their beliefs could lead to any organisation dealing with contentious matters staking a claim for a buffer zone around its premises.
"A gender dysphoria clinic could seek a buffer zone excluding those voicing concerns about puberty blockers, or a foreign embassy could request a buffer zone near its premises to prevent people speaking out against the regime. What would become criminal is whatever dissent a group wants to prosecute."