Some of the UK's best-known brands have announced that they would be reviewing their advertising in the News of the World amid a growing public backlash over the paper's hacking of Milly Dowler's phone.

Ford, npower, Halifax, T-Mobile and Orange became the first large companies to announce such action as the pressure increased on both the newspaper and those who advertise in its pages.

The energy company was the quickest to react to the fallout from the allegations, with an npower spokeswoman saying: "We note the concerns which have arisen on the back of fresh allegations of phone hacking against the News of the World. We are currently reviewing our options."

Halifax also confirmed that it was considering its options about advertising in the News of the World, adding: "We are sensitive to the views of our customers and will take them into account."

Ford went furthest, however, saying it would be using "alternative media within and outside News International group instead of placing Ford advertising in the News of the World" while it awaited the outcome of the investigation.

It added: "Ford is a company which cares about the standards of behaviour of its own people and those it deals with externally."

A spokesman for T-Mobile said: "We're currently reviewing our advertising position with News of the World, following the recent allegations, and await the outcome of the ongoing police investigation."

Orange put out a similar statement, saying: "We're currently reviewing our advertising position with News of the World, following the recent allegations, and await the outcome of the ongoing police investigation."

The companies' decisions to rethink their advertising in the paper could have a significant financial impact on it and its sister title, the Sun.

According to advertising industry estimates, npower spent £1m on advertising in the two papers in the year to the end of May, while Halifax spent £1.5m and Ford £600,000.

However, the company that spent most on advertising in the same period was BSkyB, which is 39% owned by News Corp, owner of the Wapping newspapers.

Other companies contacted by the Guardian were less forthcoming about their advertising plans, despite mounting public anger.

Virgin media said it was "awaiting the outcome of any investigation" while Cadbury Dairy Milk said: "We review our advertising strategy regularly."

A spokesman for Dixons, the electricals store, said it did not comment on specific cases but there were "a number of factors that determine our media planning and we constantly review all the media we use".

Tesco put out a statement on Facebook and Twitter in a bid to reassure its customers. While acknowledging that the revelations would "cause huge distress to a family which has suffered enough", the supermarket said the allegations were now a police matter, adding: "Like everyone, we await the outcome of their investigation."

The allegations had earlier sent social media users roaring into action, with calls for boycotts of the News of the World appearing on Twitter and Facebook, and companies coming under sustained pressure to pull their advertising from the paper.

Those wishing to direct their fury at the firms who advertise through the News of the World were provided with a one-stop page where they could automatically tweet their concerns to companies such as the Co-operative, easyJet, Butlins and Renault.

Others went further, calling for direct boycotts of the companies themselves unless they took their advertising money elsewhere.

Twitter users also posted the phone number of the News of the World's newsdesk online and encouraged people to call up and make their anger felt.

One journalist said he had been told by a News of the World employee that a succession of people were ringing the newsdesk, "shouting the c-word down the phone, and hanging up".

The Guardian media columnist and blogger Roy Greenslade gave readers a list of five things they could do to register their disapproval.

His first suggestion was a mass boycott of the News of the World: "Treat it just as the people of Merseyside did when the Sun ran its infamous Hillsborough story in 1989 following the deaths of 96 Liverpool supporters."

Greenslade, a former editor of the Daily Mirror, also added his voice to those calling for an independent public inquiry into the hacking affair.

The push for a public investigation into the matter will be launched on Wednesday at the House of Lords by a group of media academics, lawyers, MPs and peers.

Martin Moore, the director of the Media Standards Trust, which is co-ordinating the campaign for a public inquiry, said: "We've been pressing for a public inquiry for a long time, but a few weeks ago, when we started to realise that the civil cases would be closed down by November without disclosure, we realised that it was increasingly urgent to get a public inquiry."

The latest revelations, he added, had convinced the organisers that now was the time to act.

A poll on the Guardian website on Tuesday showed that 97% of respondents were in favour of a public inquiry.

However, as a few tweeters pointed out, the ethical failings exposed by the recent allegations may not have been confined to the News of the World newsroom.

One tweeter wondered whether or not the rest of Fleet Street would now think twice before picking up News of the World "exclusives".

• This article was amended on 6 July 2011. The original referred to T-Mobile's rival phone company Orange. This has been corrected.