The campaign group that encouraged Paperchase to apologise for its marketing activities with the Daily Mail is pushing for John Lewis, the department store chain, to stop advertising with the newspaper as well as with the Sun and Daily Express.

John Lewis has become a prime target for Stop Funding Hate on the back of the launch of its Christmas advert and as retailers increase their spending on advertising as the festive season approaches.

Stop Funding Hate has produced a mock advert that depicts the star of last year’s John Lewis Christmas advert – Buster the dog – as unhappy because the retailer is buying adverts with the Mail, Sun, and Express. The video has been shared almost 10,000 times on Twitter and Facebook.

Sainsbury’s, Marks & Spencer and Waitrose are also being targeted by Stop Funding Hate.

The organisation was founded last year and says its aim is to take on “divisive hate campaigns” by the Mail, Sun and Express, and persuade advertisers to cease their financial input.

Richard Wilson, the founder of Stop Funding Hate, said: “[John Lewis] are a company well known for their ethical values and one that people have a lot of respect for. Customers are saying there is a clash between what the brand stands for and these newspapers. It would be great if John Lewis made a move, but another company could make a move too.”

However, John Lewis said it would continue advertising with the newspapers and not bow to the pressure. A spokesperson said: “Withdrawing advertising on the basis of editorial coverage would be inconsistent with our democratic principles, which include freedom of speech and remaining apolitical.”

Paperchase announced on Monday that it would not run any marketing campaigns with the Daily Mail and said it was “truly sorry” for running a front-page promotion in Saturday’s edition of the newspaper. Stop Funding Hate encouraged Paperchase customers on social media to express their disappointment with the retailer after the promotion appeared.

However, Paperchase’s apology has provoked a backlash, with the Daily Mail saying it was deeply worrying that the greeting card retailer had allowed itself to be bullied by a “small group of hard-left Corbynist individuals seeking to suppress legitimate debate”.

Stop Funding Hate targets the Daily Mail, Sun and Daily Express, and claims on its website that 23 companies and organisations have now said they will not advertise with one or all of the newspapers. The list includes Lego, the Body Shop, the fashion retailer Joy, and Evans Cycles, as well as Paperchase.

The campaign group has also published lists of the top 10 advertisers in the Mail, Sun and Express, and its website includes links to the Twitter accounts of Britain’s largest supermarkets so that customers can express their concerns.

Wilson denied that Stop Funding Hate was suppressing freedom of speech or that Paperchase had been bullied, saying it had been a “civilised conversation” with the retailer. “If you look at the tweets [to Paperchase], they were very friendly overall as far I could see,” he said. “Customers have a right to freedom of expression as well and Paperchase has a right to choose where it does and does not advertise. Censorship has a clear definition and talking to Paperchase and asking them to switch advertising is not a breach of freedom of speech. No human rights have been abused by Paperchase switching from the Daily Mail. It’s a business choice.”

A spokesperson for the Daily Mail said: “All newspapers, the Guardian included, should be deeply concerned at this sinister campaign by a tiny group of hard-left, Corbynist internet activists – ardent Remainers – to use social media trolling to shut down legitimate debate in order to impose their own views on the Mail and other newspapers.

“Anyone who values freedom of expression should equally be disturbed by Stop Funding Hate’s attempts to apply commercial pressure to newspapers’ advertisers and business partners in order to influence their editorial decisions. If big business was using this tactic against the Guardian your liberal commentators would rightly be outraged.

“Stop Funding Hate’s founder, Richard Wilson, chillingly described their aims last night – ‘the end point for us is a media that does the job that we all want it to’. There you have it: an arrogant, self-appointed group of internet activists using trolling to silence a free press enjoyed by millions, and force it to promote their views alone.”

In response to the Mail’s comment, Stop Funding Hate said: “Stop Funding Hate is a non-partisan human rights campaign focussed solely on the issue of hate speech and discrimination. We have no position on any other issue.

“We are shocked at the personalised attacks that have been directed at Stop Funding Hate supporters in recent days – and at attempts by the Daily Mail and others to delegitimise peaceful protest by characterising consumer engagement as ‘sinister’ and ‘bullying’.

“For the avoidance of doubt, Stop Funding Hate is not linked to, or aligned to, any political party. We are funded by voluntary donations from thousands of members of the public.

“We are proud to have supporters from a wide range of backgrounds and political viewpoints – and welcome the support of everyone who shares our values.”