Bloggers could face high fines for libel under the new Leveson deal with exemplary damages imposed if they don't sign up to the new regulator, it was claimed on Tuesday.

Under clause 29 introduced to the crime and courts bill in the Commons on Monday night, the definition of "relevant" bloggers or websites includes any that generate news material where there is an editorial structure giving someone control over publication.

Bloggers would not be at risk of exemplary damages for comments posted by readers. There is also a schedule that excludes certain publishers such as scientific journals, student publications and not-for-profit community newspapers. Websites are guaranteed exclusion from exemplary damages if they can get on this list.

Kirsty Hughes, the chief executive of Index on Censorship, which campaigns for press freedom around the world, said it was a "sad day" for British democracy. "This will undoubtedly have a chilling effect on everyday people's web use," she said.

She said she feared thousands of websites could fall under the definition of a "relevant publisher" in clause 29.

Hughes said: "Bloggers could find themselves subject to exemplary damages, due to the fact that they were not part of a regulator that was not intended for them in the first place."

Exemplary damages and costs imposed by a court to penalise those who remained outside the regulator could run to hundreds of thousands of pounds, enough to close down smaller publishers.

Harry Cole, who works for the Guido Fawkes political blog, said it would not be joining the regulator and believes that because its servers are based in the US it will be excluded from the exemplary damages clauses.

"I don't see I should join a regulator. This country has had a free press for the last 300 years, that has been irreverent and rude as my website is and holding public officials to account. We as a matter of principle will be opposing any regulator especially one set up and accountable to politicians we write about every day," he told BBC Radio 4's Today programme.

Carla Buzasi, the editor-in-chief of the Huffington Post website, told the BBC: "I can't imagine any politician has had this discussion because they have rushed this through so quickly.

"It does worry me to a certain extent. Someone said this is a carrot and stick approach. There doesn't seem to be too much of a carrot here."

The exemplary damages clause was recommended in the Leveson report but has been opposed by newspapers, including the Guardian, which have been given legal advice that it could be contrary to the European convention on human rights, which enshrines the principle of free speech.

Lord Lester, the campaigner for libel reform, warned during the Leveson debate in the House of Lords earlier this year that publications such as Private Eye and local newspapers could face closure as a result of the imposition of exemplary damages.

On Monday night, the editor of the Guardian, Alan Rusbridger said he welcomed cross-party agreement on press regulation, but said: "We retain grave reservations about the proposed legislation on exemplary damages."

Under sustained questioning on Monday night during the Commons debate about the courts bill, which includes the Leveson regulations, the culture secretary, Maria Miller, said the "publisher would have to meet the three tests of whether the publication is publishing news-related material in the course of a business, whether their material is written by a range of authors – this would exclude a one-man band or a single blogger – and whether that material is subject to editorial control".

Miller said the new rules were designed to protect "small-scale bloggers" and to "ensure that the publishers of special interest, hobby and trade titles such as the Angling Times and the wine magazine Decanter are not caught in the regime", but Hello! magazine would be subject to regulation.

She said the "one-man band or a single blogger" would not be affected by the legislation because of the definition of "relevant publisher" in relation to exemplary damages.

Miller said "student and not-for-profit community newspapers" will not be caught under the new rules and that "scientific journals, periodicals and book publishers will also be left outside the definition and therefore not exposed to the exemplary damages and costs regime".

There was also confusion about which magazines would come under the remit of the new regulatory body. Miller said scientific journals would fall outside its scope, but the British Medical Journal, for example, is currently regulated by the Press Complaints Commission.

Sunny Hundal, editor of the Liberal Conspiracy blog, said he didn't see a cause for panic.

"There's a danger we miss the wood for the trees, as bloggers can already face big fines for libel. I'm fairly confident the eventual body will differentiate between Guardian.co.uk and independent bloggers. Trying to regulate the latter, even Leveson admitted in his final report, would be a step too far.

"The key will be to differentiate between huge operations such as Huffington Post and voluntary blogs like Liberal Conspiracy. We should be vigilant but I don't see a cause for panic yet."