HERE is a strange thing.

In the heat, hype and mild hysteria of London 2012, there was a queue of talking heads – a gaggle, if you will – who suggested that Team GB's success had ensured that the substantial cooker of Alex Salmond had been approached and his gas subsequently put at a peep.

How, they insisted, could Team SNP survive the outpouring of British joy that accompanied the medal successes of Scots such as Sir Chris Hoy, Katherine Grainger and Andy Murray, who all wrapped themselves in Union flags before bowing their heads to accept gold medals?

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Yet as the glorious summer of sport (copyright slipped into September, there was a further extraordinary drama. On a golf course just outside Chicago on a bright Sunday, Europe defeated the USA in the most dramatic day ever in the Ryder Cup. Not one talking head subsequently suggested that this victory against all odds was conclusive proof that Europe worked better as an entity and Britain should therefore join the euro forthwith, bail out Spain (which supplied a wonderful captain in Jose Maria Olazabal) and drop all attempts at isolation within the federal framework.

The lesson, of course, is that sporting occasions can be used to promote any agenda but mostly their message can be more subtle than a crude political point.

So what precisely did happen in the London of 2012? What was the story to a city that hosted a marvellous Olympics and a soggy Diamond Jubilee? The answer has to be personal. The experience of a summer in the metropolis will endure for anyone who queued to be searched, who watched the greatest show on Earth that started with the greatest opening ceremony ever or who tried to find a spot as two very old-age pensioners were taken down the Thames in a challenge worthy of the title I'm A Member Of Royalty ... Get Me Out of Here!

There were, then, at least two factors to the year of Jubilee and Olympics. The first is the royal dimension, the other is how it impacted on any individual not on the civil list.

The Diamond Jubilee was Old Royal. Elizabeth and Philip did their duty, stood to attention for what seemed like hours in the face of all that the Thames could throw at them, and smiled evenly and tolerantly at events that tried both their patience and their health.

The Olympics were New Royal: Elizabeth parachuting out of a helicopter as part of a bizarre, wonderful and Brit-affirming opening ceremony. It was an extraordinary gesture by the Queen, though cynics insisted it was performed by a stunt double. Its significance, of course, rested in the realisation that the New Royals were embracing the Olympics with a sense of fun, mischief and even competitiveness. One of them – Zara Phillips – even won a medal (in eventing).

The others – most conspicuously Harry, William and Kate, royal stars for the reality age – sat in TV studios and praised the Olympics or took seats in the velodrome, the athletics stadium, the rowing stands or at the hockey venue to cheer on what was becoming an increasingly successful British story. The New Royals were so ubiquitous that when Harry and William walked around a corner at Eton Dorney on the day of another Team GB rowing success, they were almost flattened as pressmen clambered over and around them to corner the commoner parents of a gold medal winner.

Yet their presence was a constant reminder that Britain was buying into the Games at the highest level, that all this expense for a highly inflated school sports day had been afforded by royal appointment, and that everyone should jolly well have the best of fun.

Strangely, almost everyone did. It was, perhaps, easier for the New Royals. There was a splendid moment when I watched Harry telling Gary Lineker or some other vassal that the Olympics had been so slickly organised and it was so easy to travel out to Stratford. It is when one is placed in an SUV travelling at 70mph and does not require to be searched. The lower orders were crammed into Tube trains – there was an official protest at the conditions from at least one sardine – and then faced a wait to be searched as they sought entry into the park.

These minor trials and the reaction to them became the essence of the story, the message of what London 2012 was about. People wanted to be part of something that was exciting, entertaining and novel.

They were prepared to be shoved, pulled, probed and scanned to be part of a supporting cast. London – a city I spend weeks in every year – was changed. They do not allow sex on the Tube because it may lead to a conversation. Yet last summer, passengers who did not know each other would enter into verbal intercourse. Astonishing.

This, of course, speaks to one of the outstanding successes of the Olympics: the 70,000 Games Makers. These were people who would normally seem to have been precisely manufactured to annoy a London commuter. Dressed in garish outfits, they stood on corners with giant foam hands or packs of information and, well, were, damn them, cheerful. They were also informative and genuinely welcoming. Glasgow 2014 needs to corral this particular bandwagon.

The other lesson from London was contained – as the best education is – in an extravaganza of entertainment. Danny Boyle's opening ceremony was so outlandish in action and execution that it surely would have failed a drugs test. However, it had – a parachuting Queen aside – a most serious purpose. It was a loud yet thoughtful celebration of Britain, of its music, its films, its literature and its history, including the industrial revolution and the setting up of the flawed but irredeemably magnificent, life-enhancing, life-preserving National Health Service.

We Scots, whether favoured wonderfully by fate to sit in the arena or restricted to watching it on television, would not find it difficult to accept that this spot in east London that was forever England also carried a strong Caledonian resonance, and not just in performers or in marching athletes.

The joy of the London Olympics was that it embraced all on this island, Nationalist or Unionist. It was as easy to cheer British success as it was to roar a month a later when a German made the winning put in the Ryder Cup for Europe.

The political implications were more than a tad overstated as commentators looked at the proliferation of Union flags and predicted perdition for Salmond. This observer – who will vote for independence in any referendum – was delighted at the success of Team GB, and uplifted by the Scottish achievements under the Unionist flag.

The reality is, of course, that everyone wants to be part of something bigger. The reality, too, is that an independent Scotland would still be joined, at least geographically, with England, and would still be a part of Europe. This Scot looks forward to moving out of a relationship that has become cramped, outdated and unsatisfying.

But London 2012 showed me the value of what we once shared and created together. Much of that will endure whatever way Scotland votes in 2014.