It is said of Harold Wilson that he epitomised the quip: “If you can’t ride two horses at the same time, you shouldn’t be in the circus.” He was often criticised for putting pragmatism before principle in his 13 years as Labour leader, but it was an attribute that served him well in preventing the party from tearing itself apart on Europe in the 1970s.

When Wilson won a fourth general election on 10 October 1974, he faced the challenge of navigating Labour’s deep divisions on whether or not to reverse the 1972 decision to join the common market. The party’s election manifesto had promised the British people a “final say” on Britain’s membership without committing itself one way or another to a recommendation. “It is as yet too early to judge the likely results of the tough negotiations which are taking place,” it said.

Wilson did not commit himself to a definite conclusion for another five months. Tony Benn, who was secretary of state for industry at the time, records in his diary that Wilson told the crucial cabinet meeting on 18 March 1975 that he was “persuaded 51% to 49% ” to support the renegotiated membership terms. “I had anxieties right up to the last few days, but I now recommend that we stay in,” he said.

With the referendum set for 10 June 1975, Wilson had left it until the vote was less than three months away to announce that he would back the deal he had negotiated. His positioning as an honest broker was not only politically astute, it was also credible because he was not associated with either of the contending camps, both of which saw the common market membership issue as a matter of principle.

Labour’s current policy is similar to the approach Wilson took 44 years ago. Jeremy Corbyn says a Labour government would give people the final say in a public vote between “credible options for both sides”; namely, the best deal it can get from the EU – based on the policy in Labour’s 2017 manifesto – and remaining in the EU.

Corbyn has, much to the frustration of some, doggedly pursued an attempt to unite people across the Brexit divide through a deal that protects trade and standards. And this now puts him in a position akin to Wilson’s as someone who can credibly act as an honest broker in giving people a final say.

Facebook Twitter Pinterest Harold Wilson and his wife Mary campaigning before the 1974 general election Photograph: Bettmann Archive

The problem for Labour, however, is that some of the other big hitters in the shadow cabinet have now nailed their colours firmly to the remain mast. While this is as much their prerogative as it was for the opposing protagonists in 1975, it does make it harder to sustain the argument that they could negotiate effectively with Brussels.

As Emily Thornberry found on Question Time last week, it is easier for political opponents to ridicule Labour’s position if the party is suggesting that the negotiations would be led by people committed in advance to rejecting their outcome. It makes sense for Labour to make clear its team will be made up mainly of ministers who are seen to be open minded about the potential benefits of a deal.

Remainers argue, of course, that there is no better deal than the one we’ve got and, because of that, to pursue negotiations is itself disingenuous. Forget Wilson, they would no doubt say, Labour should simply campaign to reverse the 2016 decision.

Let’s leave aside the potentially suicidal electoral implications of that position. There is a case for saying a new deal with the EU could be better for working people than being a member.

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For a start, no economic modelling has been done for a situation in which government is paralysed indefinitely by Brexit gridlock, but we have already seen the negative impact of so much uncertainty. If it drags on for many more years, the effects could be far worse than any of the official scenarios published so far.

Equally, no one can say for sure what the upside benefits are of a Labour government being less constrained by state aid and competition rules than it would be as a member – but the fact that many remainers also argue for reform of these rules acknowledges there is a problem.

And no one can accurately quantify the political and social dividend that could accrue from securing a new relationship with Europe that gains the consent of both leave and remain voters.

The option of a credible deal surely, therefore, has to be pursued in good faith, but would Brussels have any incentive to offer something better than May negotiated when their preference is bound to be for the UK to remain in the EU?

The big problem with May’s approach was her desire to open the door to deregulation of the economy. For Brussels, this represented a competitive threat. But that does not arise with Labour, which sees EU employment rights and consumer and environmental protections as something to build on rather than destroy. This in itself should make it much easier to agree on a new trading relationship, including a resolution to the Irish border issue.

If Labour won an election on a pledge to negotiate a new deal and put it to a public vote, Brussels would be wise to offer something that protects the economic relationship rather than pinning everything on remain winning a majority.

Remainers might want the EU to offer an unattractive package, but it’s more likely they will see the merit in hedging their bets by giving British voters a choice between staying members or leaving on terms that they can live with.

It may be counterintuitive in the midst of this crisis, but a Wilsonian approach on Labour’s part could produce an outbreak of pragmatism on both sides of the Channel. If it does, that would allow the public to choose between two credible options, thus increasing the chances of the outcome commanding broad support. Like Wilson, Corbyn would not have to decide his recommendation until the final details of a new deal are known.

• Steve Howell is author of Game Changer: Eight Weeks that Transformed British Politics. He was deputy director of strategy and communications for Labour leader Jeremy Corbyn in 2017