This weekend, as you perhaps struggle to remember to put your watch back an hour, it may have escaped your attention that the EU has launched ambitious plans to put an end to summer and winter time.

European commission president Jean-Claude Juncker proudly announced that “clock-changing must stop”. And Euro MPs (never to be outdone by the commission) passed a resolution saying it is “crucial to maintain a unified EU time regime”. While we know from our daily diet of Brexit debates that the EU has standardised a lot in Europe, it has so far not managed to harmonise time. But the Juncker legislation now working its way through Brussels would put an end the biannual ritual of moving the clocks forward or back.

In an added twist, the proposal leaves individual EU nations to decide whether to live on summer or winter time, so potentially this law, if agreed by EU governments, is a first step to a single European time.

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Britain’s one-hour time difference with most of the EU, two hours with Greece and Finland, is a real – if little mentioned – barrier to frictionless trade. Phone calls go unanswered, deadlines get missed. It may be only 4pm in London, but in Athens it’s 6pm – so there’s no point trying to trace that missing feta delivery.

The real costs to British business run into many millions. Time has always been a variable concept in the corridors of Brussels power. The old EU practice of “stopping the clock” in negotiations is legendary. If a midnight negotiation deadline approached, and it got to quarter to twelve with no deal in sight, the two sides could simply agree to stop the clock. I remember stories of negotiations when the clock didn’t move for days. Although, if at 11.45pm on 29 March next year, British and EU negotiators find themselves deal-less in the Brexit talks, stopping the clock won’t be an option, since the UK’s EU Withdrawal Act enshrines that Britain leave the EU at midnight Central European time (so Brexit will actually have happened an hour earlier in the UK).

With all this temporal confusion, is there not the opportunity for a great British gesture? A chance to show that post-Brexit the British not only want to stay close friends with our European neighbours, but that we would like to make their and our lives easier. Theresa May could announce that next March, when the clocks go forward – just two days after Brexit – we will at least in one respect become more European, by shifting to Central European time.

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This could even be one of the few things that the country could rally around in our national Brexit row. And we might find that one element of our lives with Europe involves actually less friction rather than more. Time could become – if not the great healer – at least a balm on our Brexit sore.

But as with so much to do with solving our European dilemmas, obstacles could come from two directions. First, the French. If Britain moved to Central European Time, there is nothing to stop French leader Emmanuel Macron using Juncker’s new law to fix France permanently on its summer time – keeping the French with their one-hour lead, and once again thwarting the British.

And then there are the ultra Brexiteers. Jacob Rees-Mogg once tabled an amendment in the House of Commons calling for Somerset to have its own time zone. The ultra Brexiteers may yet hold May to ransom, and insist that Europe move to British time – rather than the other way around.

• Nigel Gardner is a former European commission spokesman, and last year produced BBC2’s documentary series on Britain’s troubled history with the EU