Jeremy Corbyn, the surprise frontrunner for the Labour leadership, is regularly attacked by his opponents as a political throwback to the days of trade union militancy and the Bennite hard left.

In fact, his ideals are of an even more venerable vintage than that: they are rooted in the radical thought of mid-17th-century England. Asked in an interview with the New Statesman to identify the historical figure he most admired, Corbyn named John Lilburne. Paradoxically, it is this that makes Corbyn so well attuned to the current political zeitgeist.

Probably born in 1615 in Sunderland, Lilburne was apprenticed to a puritan clothier in London, which brought him into contact with leading opponents of King Charles I’s religious policies. His political career began when he was arrested for distributing illicit pamphlets highly critical of Charles’s bishops in 1637.

Tried by the Star Chamber, he was sentenced in February 1638 to be whipped from the Fleet prison to New Palace Yard, then put in the pillory. There, Lilburne used his punishment as an opportunity to further the puritan cause, denouncing the court and the episcopate so vehemently that he had to be gagged to prevent further outbursts. Though silenced, he continued to frustrate the authorities, distributing pamphlets and later authoring accounts of his sufferings when returned to jail.

Freed from prison in 1640 through the intervention of Oliver Cromwell, Lilburne would forge a career as one of the most prominent radical figures of the period. Along with the works of other writers, notably Richard Overton, William Walwyn and John Wildman, Lilburne’s ideas formed the intellectual basis for what came to be known as the Leveller movement.

The Levellers’ ideals were crystallised in the movement’s “manifesto”, An Agreement of the People, first published in 1647 and discussed at the famous Putney debates of the same year.

The agreement envisaged a dramatic transformation of England’s ancient constitution: the House of Commons would be replaced with a new representative body, elected through a reformed voting system (at Putney, interpreted to mean male suffrage) with new elections every two years.

The interest in the radicalism of the English revolution is indicative of the current crisis in British political life

The new elected body would be the sovereign authority in the land, but the Levellers were committed to the idea that all power ultimately resided with the people. Hence the agreement outlined certain rights, including freedom of conscience and equality under the law, which neither legislative nor executive power could infringe.

It might be tempting to see Corbyn’s fondness for Lilburne as as much about personality as politics. Just as Corbyn has been depicted as a perpetual rebel, persistently defying the party whips over his 22 years in parliament, so Lilburne developed a reputation as an inveterate troublemaker. According to Lilburne’s contemporary, the MP Henry Marten: “If the world was emptied of all but John Lilburne, Lilburne would quarrel with John and John with Lilburne.”

Corbyn, an acolyte of Tony Benn, who was a great populariser of the Levellers’ ideas, is exactly the sort of leftwinger you would expect to celebrate these English radicals. It was certainly no shock to see him speaking this year at an event commemorating the 400th anniversary of Lilburne’s birth.

But Corbyn is not alone among modern politicians in his admiration for the Levellers. In 2012 the Labour MP Tristram Hunt described the then Tory and now Ukip MP Douglas Carswell as a modern-day Lilburne. The comparison was doubtless meant in jest, alluding to the degree to which Carswell was a persistent thorn in the side of David Cameron. However, Carswell had already written glowingly about the Levellers two years earlier on his blog, seeing them as proto-Conservatives who favoured small government, low taxes and free trade.

Carswell’s presentation of the Levellers was just as anachronistic as leftwing depictions of them as “Britain’s first socialists”. Yet the interest in the radicalism of the English revolution from figures across the political spectrum (the MEP Daniel Hannan is another Tory Lilburne fan) is significant and indicative of the current crisis in British political life.

The British parliamentary system is typically presented as the product of centuries of gradual constitutional change. Dramatic ruptures, such as the civil wars, are normally glossed over. But as this system – like the Palace of Westminster itself – falls apart, the English revolution, the last time when radical alternatives to our ancient constitution were seriously discussed, suddenly appears relevant again.

The current thirst for more direct forms of democracy – e-petitions, referendums, the right to recall – resonates with ideas and strategies first deployed by the Levellers, from the plebiscites that would confirm public acceptance of the Levellers’ agreement, to the idea of MPs as no more than the “agents” (delegates) of their “principals” (the people).

The radicalism that flourished in the mid-17th century, often marginalised in national public memory, is once more in vogue. Even Corbyn’s centrist opponents are desperate to claim the radical label.

Corbyn is certainly not Lilburne reborn. But “Corbynmania” represents something more than a bizarre personality cult or a collective political death wish. Corbyn’s goal of reinvigorating Labour as a social movement has a powerful appeal.

In Corbyn, who is an activist as much as a parliamentarian, the public has identified a figure who can bridge the gap between the old politics and the new. Much of the “new” politics, however, has its origins in the 17th century and the solutions and tactics first advocated by “freeborn John”.