Laws that led to London being dubbed "the libel capital of the world" will be reformed after peers in the Lords voted to pass the defamation bill, ending a three-year campaign led by Liberal Democrat peers Lord McNally and Lord Lester.

Libel reform campaigners said they were "delighted" overall that defamation reform was finally passing into law, although they were disappointed by the failure of a bid to bar private companies contracted to run schools, prisons or healthcare from suing ordinary citizens who criticised the work they do for the taxpayer.

However, the bill is a landmark piece of legislation and should provide more protection for individuals and organisations, including newspapers and broadcasters, which criticise big companies.

The new law will also stop cases being taken in London against journalists, academics or individuals who live outside the country, denting the libel tourism industry, but not ending it altogether, as foreigners will still be able to lodge claims in the high court.

Peers voted by a majority of 78 to pass the bill, which means it will now return to the Commons on Wednesday for formal approval with no possibility of fresh amendments.

It is believed that all but one Liberal Democrat peer had sided with the Tories, dashing Labour's chances of tightening up the rules on private companies contracted by local councils or government departments from suing without showing they have suffered "substantial financial loss" before taking legal action.

Labour peer Baroness Hayter said there was concern this would deter members of the public from airing grievances or criticising "a wider – and growing – ring of organisations contracted or commissioned to provide public services".

These ranged from independent treatment centres to opticians, dentists, GP consortia treating or diagnosing NHS patients, private organisations providing care homes, school dinners or prison management, Hayter added.

As the law stands, local councils are banned from suing for libel in relation to the execution of their public duties and Labour had tabled an amendment that would extend this to all third parties, but was defeated in Wednesday's Lords vote.

Kirsty Hughes, chief executive of Index on Censorship said she was "delighted" that corporations will now have to prove financial loss before they sue for libel but added it was a "pity" the government voted against Labour's amendment to stop public money being used to stop "citizen critics".

Gillian Slovo, novelist and daughter of anti-apartheid campaigner Joe Slovo, heralded the campaign as a victory for those across society who had campaigned for the reforms of "an arcane law".

'We didn't get everything we fought for, but we can say at the end of more than three years campaigning that there will be significantly less chill on freedom of expression," she said.

Jo Glanville, director of English Pen, which campaigns to uphold writers' freedoms around the world, said: "We are delighted all in all, but obviously are very disappointed with the increasing privatisation of services that it did not go far as we would have liked on private companies being able to sue. This will have a chilling effect on free speech as they use the law to bully in a way they have done in the past."