ON the night of the 28th October 1971, not long after the House of Commons voted in favour of the UK joining the European Community, the then Prime Minister Edward Heath retired to Number 10 to celebrate his victory. Sitting down at his clavichord, he played the first prelude from Bach’s Well-Tempered Clavier. “It was the right choice for that moment,” he later wrote in his memoirs. “At once so serene, so ordered and so profound.”

Forty-seven years on from that revealing little moment in political history, Theresa May now faces a vote of her own in the Commons to pretty much undo all of Ted Heath’s work and it makes you wonder what music might be appropriate this time round. Messiaen’s Quartet for the End of Time perhaps. Or John Cage’s piece for organ, As Slow as Possible, which takes 639 years to perform. Or maybe even Eh-Oh by the Teletubbies. Any of them might symbolise the mess we’re in now: the disorder, the division, the dragged-out damage.

To make some sense of it all, it might be useful to remember what Edward Heath thought he had achieved in 1971 as well as the approach he took to some of the controversies that are still with us, such as referendums. Mr Heath said in ‘71 that he believed the British people would eventually see the wider benefits of the European Community, particularly peace and prosperity. “I believe they will become convinced that this is where the future of modern Britain lies,” he said.

For a while, they did, although Ted Heath did have to fight hard to win a majority in the Commons. He also resisted the pressure to hold a referendum, which some said was the only way to avoid the claim that the Government was dragging the country into the Common Market against its will. Mr Heath took a view that now looks impossibly elitist or hugely realistic: in a parliamentary democracy, he said, it would be irresponsible to leave a decision on so critical and complex an issue to the electorate.

It obviously wouldn’t be easy for a politician to express that kind of view now, but there are lessons for Theresa May to learn from Ted Heath’s experiences – not easy ones though. Specifically, in one respect Mrs May (or whoever succeeds her) needs to do exactly the same as Ted Heath did, which is to aim for the reasonable centre of the electorate, which still exists and which supports remaining in the EU, a soft Brexit, or some pragmatic compromise.

However, it now looks like she can only achieve that result if, in another respect, she does exactly the opposite to Ted Heath. Heath thought referendums contradicted the principles of parliamentary democracy – and they do – but in the circumstances we’re in, another public vote is the only way to get us away from the extremes of Brexit. In fact, a second vote may end up being one of the few redeeming features of this process by recalibrating us back to where all the good and sensible stuff happens in politics: the centre ground.

It is likely to happen because of the logistics of where we are. Theresa May did not – and realistically could not – stick to her Remain principles when she took over as leader of the Conservative party, but she has achieved the best deal in the circumstances – some of which were unavoidable, some of which were self-inflicted.

The unavoidable bit was the UK’s border with Ireland – a hard border is impossible without being a member of the customs union – whereas the self-inflicted bit was Mrs May’s insistence on ending the free movement of people, which ruled out membership of the single market. In this version of our world – part reality, part unreality created by Mrs May – the deal we have is the only practical option.

All of that means that the next few stages in the process are pretty much inevitable. Mrs May is still trying to appease Brexiters by promising that a wonderful free trade deal is still on the horizon but unless we can reach a deal that avoids a hard border in Ireland – and no one has come up with one – then, under Mrs May’s plan, Britain will eventually enter the backstop outlined in the withdrawal agreement. Realistically, the backstop is also likely to form the basis of the long-term relationship between the UK and the EU: in other words, a UK-wide customs union with Northern Ireland retaining some elements of the single market.

However, we know, and Mrs May knows, that there is no majority in the Commons for that, which leaves only four options: three unlikely and one almost inevitable. The unlikely options are, first, a no-deal Brexit (but again there’s no majority in the Commons for that); second, a re-negotiation of the deal, which the EU has already ruled out whatever Andrea Leadsom says; and third, a general election, which neither Theresa May nor any other Tory PM would go for.

Which leaves us with the fourth option: another referendum. Ted Heath was right to resist one when he was PM, but 47 years on, another public vote will soon be Mrs May’s only choice. She cannot appeal to the right-wing extremists who think the same way about Brexit as some Christian evangelists think about gay-cure therapy – that the facts of life can be changed by faith. In insisting on her version of Brexit, she has also ruled out support from the hardcore Remainers and the SNP.

However, in (consciously or unconsciously) creating a situation where a second vote on Brexit is now the only option, Mrs May could be doing us all a favour. There is always a chance the result will be another vote for Leave, but the polls show a vote for Remain is increasingly likely. If so, that could help quieten the extremists of all kinds – Brexiter, Socialist, Northern Irish Unionist and Scottish Nationalist – and take us back to the centre of politics. A good result in a second referendum on Brexit might also achieve a little of what Edward Heath felt in Number 10 on the evening of 28th October 1971: a sense that the world is in the right order, a feeling that we are doing what’s best for Britain, and maybe even some longed-for peace of mind.