After Edward Snowden revealed that the UK's security agencies are developing bulk surveillance of our metadata, a number of people said Britain needs a "fourth amendment" to protect our privacy from "unreasonable searches".

When the Guardian was threatened by the government for publishing the Snowden revelations there were demands for a British "first amendment" to entrench freedom of the press. Now that the British state is holding secret trials there is talk of the need for a sixth amendment, that anyone accused "shall enjoy the right ... to be informed of the nature and cause of the accusation", or even the fifth, that no one should be "deprived of life, liberty, or property, without due process of law".

But there is ascreamingly obvious problem with all such demands: we do not have a constitution to amend. We cannot extend or strengthen our basic rights as we do not have such rights, they remain gifted (and able to be taken away) by a sleepy, if not intoxicated, parliament.

We do have a constitution, of course. Peter Hennessy, now a crossbench peer, once took his students to meet Sir Robin (now Lord) Butler, then cabinet secretary and head of the civil service. One of them innocently asked what is the British constitution. Butler answered: "Something we make up as we go along."

Who is this "we"? It's certainly not "We, the people". When Butler was speaking he was part of the last remnants of the old establishment; now the British constitution is something GCHQ makes up as it goes along.

Sunday marks the 799th anniversary of the granting of Magna Carta at Runnymede, on 15 June 1215. Those fifth and sixth amendments trace their antecedents back to Magna Carta's assertion that a freeman may not be condemned "except by lawful judgment of his peers". Conceded under duress, the charter held a monarch to account. In so doing it wrote down on parchment how we are to be ruled, rather than leaving things to the informal instincts of generations of Robin Butlers.

Though now rarely acknowledged, it was dubbed Magna Carta, or the Great Charter, for a specific reason. It linked the document to its minor companion, the Charter of the Forests, which set out the rights of access and use of the public commons. It even, it has been argued, imposed an ecological commitment to their maintenance. Finally, the Great Charter enshrined claims to due process and trial by jury, pillars of the rule of law that today are openly regarded as impediments to national security.

Thus, any authentic celebration of Magna Carta would be a sober, serious challenge to the status quo, unlike the official website that cannot bring itself to reproduce the actual Magna Carta, let alone the Charter of the Forests.

This is not to claim that Magna Carta was "progressive". It was a feudal deal. It's the myth that matters: an inspiration to challenge arbitrary, despotic power; a seed for a democratic constitution; a right to be ruled by law; and even a claim that land be held in common, not enclosed for profit.

To snuff out all such radicalism, the official celebrations of its 800 years will be funded 12 months hence by £1m from chancellor George Osborne, and we will be palmed off with an assortment of Magna Balls to express gratitude to Britain's ruling order gifting liberty to the globe.

That is how Margaret Thatcher saw it. In 1990, unable to prevent the unification of Germany, she planned to use a November summit in Paris on European security to launch a Magna Carta for eastern Europe. At the press conference I asked her: "Why, when you called upon this summit to entrench rights across Europe, do you not agree with [my pressure group] Charter 88 that we should have entrenched rights in the UK?" She replied: "We are in this summit to get rights way across the European divide … to call for the community to extend democracy to other countries."

Within three days British democracy forced Thatcher to resign. Let's hope the curse of Magna Carta brings down our present bunch of manipulative populists. Eight hundred years of rule by barons is enough. It is the peoples' turn for a document that protects our democracy, our liberty – and now our metadata.

• This article was amended on 16 June 2014 to clarify that Magna Carta was granted rather than signed.