Lord Carey says plans would cause deep divisions and likens opponents of gay marriage to Jews in Nazi Germany

The former archbishop of Canterbury, Lord Carey, has accused David Cameron of "plundering" the institution of heterosexual marriage to promote same-sex marriage rights. Allowing gay marriage would cause deep divisions in society "without giving gays a single right they do not have in civil partnership", he said.

At a Coalition for Marriage rally on the fringe of the Conservative conference in Birmingham on Monday, Carey joined David Burrowes, the backbench MP for Enfield Southgate, and former MP Ann Widdecombe in protesting that neither the Lib Dem nor Tory 2010 manifesto included a pledge to legalise gay marriage.

Carey claimed that in some countries where same-sex marriage had been made legal – including Mexico, Brazil and the Netherlands – it had led to unforeseen consequences such as three-person marriages.

Asked about opponents of gay marriage being described as "bigots" – on one occasion by Nick Clegg, the deputy prime minister – Carey said: "Let us remember the Jews in Nazi Germany. What started against them was when they started to be called names.

"And that was the first stage towards that totalitarian state. We have to resist them. We treasure democracy. We treasure our Christian inheritance and we want to debate this in a fair way."

Widdecombe said: "This is not an anti-gay rally. It is defending marriage."

Outside the town hall rally, attended by about 400 people, gay rights protesters accused the platform of promoting "marriage apartheid" by denying the right to marry on equal terms.

Cameron has joined the US president, Barack Obama, in endorsing same-sex marriage and is poised to report on the results of a 12-week consultation before proceeding to legislate. All main parties, including the SNP government in Edinburgh, now endorse the change.

Burrowes urged ministers to stage a referendum on the issue, as has been done in 32 US states with mixed results. He said there had been no pressure for a change to civil partnership before the election – "no letters, emails or tweets" from voters – but MPs' postbags were now full of the controversy. "If the government can think again about pasties and caravans it can certainly do so about the important issue of marriage," he said.

Widdecombe, a former Home Office minister, said such consequences would include the replacement of cherished liturgy and names such as "mother" and "father" with "progenitor A and progenitor B" or "partners to the marriage". François Hollande, the French president, was proposing to use the word "carers", she said.

Carey argued that teachers, doctors and other professionals might be forced out of their jobs if they refused to embrace the proposed change to the law, an intolerant restriction on free speech that Widdecombe said could make the Church of England force disestablishment.

"I know, David Cameron, that is not the sort of Britain you want," she said.Carey hinted that the prime minister might have conceded the policy on "pragmatic" grounds to sustain his coalition with the Lib Dems – "the very worst of reasons".

Ben Summerskill, the chief executive of gay rights group Stonewall, said: "We're deeply saddened that Lord Carey seems to be resorting to student union abuse. The reality is that gay people are very well aware of the consequences of the Holocaust, for obvious reasons, and when someone descends to this level of rhetoric it suggests they don't think they have very powerful arguments to rely on.

"Lord Carey is perfectly entitled to his view and we respect that. It's the view of many people of his generation and we accept that, but to compare Cameron to Hitler is just sad as well as being entirely inappropriate.

"It's extraordinary that he should resort to this sort of invective and profoundly unchristian. There will be gay people of faith who are very disturbed by what he has said.

"The argument is lost already but that doesn't mean the battle won't be a rough one when the time comes. But it is surprising they couldn't come up with a more persuasive argument for this, the apex of their campaign for which they have had had plenty of time to marshall their arguments."