A law banning "insulting" words or behaviour should be removed in an effort to protect free speech, MPs and civil rights groups have said.
The Public Order Act prohibits such actions if they are deemed likely to cause "harassment, alarm or distress".
A student was reportedly arrested for calling a police officer's horse "gay".
Senior Conservative David Davis said the law - which the government is looking at changing - could have a "chilling effect on democracy".
He argues the measure, as laid out in Section 5 of the 1986 Public Order Act, offers no clarity on what constitutes insulting behaviour.
There have been several controversial cases in recent years:
- In 2006, an Oxford University student asked a mounted police officer if he realised his horse was "gay" during a night out with friends after his final exams. He was arrested for making homophobic remarks after he refused to pay an £80 fine and spent a night in a police cell before charges were dropped.
- City of London police charged a teenager for demonstrating outside the London headquarters of the Church of Scientology in May 2008 with a placard saying: "Scientology is not a religion, it is a dangerous cult." Charges were dropped when the Crown Prosecution Service ruled the word "cult" was neither "abusive or insulting".
- In 2009, Christian hoteliers were accused of asking a Muslim guest if she was a murderer and a terrorist because she was wearing a "hijab". After a two-day trial, a district judge dismissed the case on the basis that the account of the prosecution witness could not be relied on.
The Reform Section 5 campaign, being launched by Mr Davis in Parliament on Wednesday, includes the Christian Institute and the National Secular Society among its supporters.
A ComRes poll it commissioned suggests 62% of MPs think it should not be the state's job to ban insults, while 17% said changing Section 5 would undermine the police's ability to protect the public.
Mr Davis, a former shadow home secretary, said a legal change was "vital to protecting freedom of expression in Britain today".
He added: "Who should decide who is insulted? The police? A judge? The truth is that Section 5 is having a terrible, chilling effect on democracy today."
Gay rights campaigner Peter Tatchell, another supporter of Reform Section 5, told BBC Radio 4's Today programme: "What constitutes insults is a very subjective judgement. It's been used in very different ways."
He added: "We may disagree on some those views but I don't think they should be criminalised in a free and democratic society.
"We should have the right to speak our minds and I think putting up with insults is one of the prices we pay for that freedom."
Mr Tatchell, who said he had been arrested under Section 5 for protesting against "Islamic extremists", added: "There's no requirement under the law to prove that anyone has been harassed, alarmed or distressed. A likelihood is sufficient to secure a conviction.
"What's dangerous about this law is that an offence is committed regardless of the person's intention."
Other groups signed up to the campaign include Liberty, Big Brother Watch and the Freedom Association.
A Home Office review, launched last October, is looking at whether the use of the word "insulting" in the law provides a "proportionate" response and a "necessary balance between the right to freedom of expression and the right of others to not be harassed, alarmed or distressed".