Britain should introduce its own constitution with an enshrined right to freedom of speech similar to that of the US to ensure that whistleblowers can come forward, Wikipedia founder Jimmy Wales has said.

He said that doing so would help prevent governments from cracking down on media organisations that wanted to publish potentially damaging stories.

"One of the big differences between the US and the UK is the first amendment, so the idea of smashing computers in the basement of the New York Times is basically inconceivable," he said, referring to the British government's demand that the Guardian destroy hard-drives used to store Edward Snowden's secret files.

"One of the important things about the US is that something like the first amendment and the rest of the Bill of Rights is very difficult to change – whereas here, it's not so easy to construct something that's difficult to change. Parliament can ultimately change anything with a majority vote and that's that."

Wales was speaking to the Guardian on Saturday at a London summit marking the anniversary of the start of Snowden's revelations, which were first published in the Guardian and the Washington Post.

Saturday's day of action was billed as the biggest privacy event of 2014, with more than 500 people attending in east London.

The Wikipedia founder's call for a "British first amendment" echoed that of the Guardian's editor-in-chief Alan Rusbridger, who was ordered to destroy the hard-drives by the government under threat of legal action.

Rusbridger said no right to free speech is enshrined in British law and said that he felt a "sense of foreboding, that something bad would happen" in the UK in reaction to the Guardian publishing Snowden's material.

He said he had no such concerns about the US government because of the protections afforded by that nation's constitution.

"By forcing the reporting out of the UK to the US, the British government lost any handle on this story at all. So, I hope the British government will think about that in the future," he said.

Wales, Rusbridger and a host of other speakers addressed a packed Shoreditch Town Hall on Saturday on the subject of privacy in the wake of Snowden's revelations of industrial-scale spying by the UK and US governments.

The event has been organised by the Guardian and the Don't Spy on Us Campaign, a coalition of privacy, free expression and digital rights organisations which is urging the UK government to end the mass surveillance of the web and mobile phone networks by the British eavesdropping centre, GCHQ.

The day started with a video address from performer Stephen Fry, who called the government's actions in spying on its own citizens "squalid and rancid".

In a prerecorded address, he said: "The idea of having your letters read by somebody, your telegrams, your faxes, your postcards intercepted, was always considered one of the meanest, most beastly things a human being could do, and for a government to do, without good cause.

"Using the fear of terrorism that we all have, the fear of the unknown that we all share, the fear of enemies that hate us, is a duplicitous and deeply wrong means of excusing something as base as spying on the citizens of your own country," he said.

Fry added: "It's enough that corporations know so much about us and our spending habits, our eating habits, our sexual preferences, everything else.

"But that a government, something that we elect, something that should be looking out for our best interests, should presume without asking to take information that we swap, we hope privately, between ourselves is frankly disgraceful."