The Defence Secretary gave the stark warning after the House of Lords voted in favour of proceeding with part two of the Leveson Inquiry into press standards.
If enacted, legislation under Section 40 of the Crime and Courts Act 2013 would require newspapers not signed up to an approved regulator to pay their own and their opponents’ legal costs in libel cases.
The only regulator currently recognised by the Press Recognition Panel (PRP) is Max Mosley's Impress, which has signed up less than 100 publications – most of them small news websites and accompanying print editions.
Mr Williamson said today: "All Section 40 is going to do is destroy the local press and take away a local voice for so many people around the country.
"That is why it is vital we get rid of Section 40 and ensure we give local newspapers the opportunity to dig out the facts that need to be revealed.
"Anyone who voted for Section 40 is voting to get rid of their local newspaper."
Theresa May has said the legislation 'would undermine high-quality journalism and a free press'.
“I think it would particularly have a negative impact on local newspapers, which are an important underpinning of our democracy," the Prime Minister added.
“I believe passionately in a free press. We want to have a free press that is able to hold politicians and others to account and we will certainly be looking to overturn this vote in the House of Commons.”
Culture Secretary Matt Hancock has accused peers of attempting to restrict press freedom, describing their votes as a 'hammer blow to the local press'.
But Labour’s deputy leader, Tom Watson, the MP for West Bromwich East, has criticised their comments, accusing the Prime Minister of abandoning 'all the promises made to victims after the hacking scandal was exposed'.
Leveson 2 would look into the relationship between the media and the police.
The Government is currently considering submissions to a consultation on whether to go ahead with Leveson 2 and Section 40.