The Conservative minister James Cleverly has criticised ice-cream company Ben & Jerry’s for “virtue signalling”, after the company spoke out on social media about the plight of migrants and refugees attempting to cross the Channel.

The spat between the ice-cream manufacturer and the government began when the company’s social media team published a thread about migrants and refugees directed at the home secretary, Priti Patel. Starting “the real crisis is our lack of humanity for people fleeing war, climate change and torture”, the thread pulled together a series of facts and resources about asylum seekers.

“People cannot be illegal. And, it is enshrined in the 1951 Refugee Convention that crossing a border ‘illegally’ should not impact your asylum claim,” the company tweeted, in reaction to a lengthy thread posted by Patel.

In her tweets last Friday Patel had described as “shameful” the number of boats crossing the Channel, which she also called “appalling and unacceptably high”, adding that they were breaking the law by travelling to the UK.

Home Office sources said: “Priti is working day and night to bring an end to these small boat crossings, which are facilitated by international criminal gangs and are rightly of serious concern to the British people. If that means upsetting the social media team for a brand of overpriced junk food, then so be it.”

Hours after Ben & Jerry’s tweets, Cleverly entered the fray, tweeting: “Can I have a large scoop of statistically inaccurate virtue signalling with my grossly overpriced ice-cream please.”

Cleverly did not specify which part of the Ben & Jerry’s thread he believed to be statistically inaccurate. His current role is as minister of state for the Middle East and north Africa, with responsibilities for “conflict, humanitarian issues, human security”.

Social media users have widely criticised coverage of the Channel crossings, particularly footage of journalists pursuing a small number of asylum seekers at sea in dinghies.

Response to the ice-cream spat has divided along predictable lines on social media, with some users calling for a boycott of Ben & Jerry’s, and others claiming they were going out specifically to purchase in support of the company’s stance.

Ben Cohen and Jerry Greenfield founded the ice cream company in 1978, and it gained a reputation for being a social enterprise that prioritised both people and profits in what the pair dubbed the “double dip”. Based in Vermont, the company was sold to Unilever in 2000, but has remained socially active on a range of issues.

Founder Ben Cohen has independently released a flavour with a political message, 2016’s Bernie’s Yearning in support of Bernie Sanders’ attempts to win the Democratic nomination to run for president, and in 2018 the company released Pecan Resist, an anti-Trump flavour. Earlier this year the company vocally supported the Black Lives Matter movement in both the UK and US.