Largely below the political radar, Scotland's premier city has been quietly carving out a new agenda well away from the hothouse of a Holyrood parliament and the great independence debate.

With the Commonwealth Games opening in Glasgow today, the city is on a roll. But the wide range of new sporting facilities – aquatic centre, velodrome, arena, for instance – and an impressive legacy programme promising thousands of new jobs are just part of a bolder initiative. Reconnecting with the UK is high on the agenda.

Glasgow city council, and seven surrounding authorities, have forged a strong relationship with England's eight largest cities, represented in the powerful Core Cities Group – and, more significantly, with the Westminster government. In a bold move, it has approved an English-style "city deal" that promises to deliver over £1.1bn in job training schemes and new infrastructure projects – such as a long overdue rail link to Glasgow airport, shelved by the SNP government in Edinburgh. "Historically, economically, socially, politically, geographically, the fact is that we have more in common with English cities than with the rest of Scotland," says Glasgow city council leader Gordon Matheson.

Glasgow has an expanding economy: a retail sector second only to London, a financial services base larger than Edinburgh, a vibrant cultural scene, outstanding scenery on its northern doorstep and it still has shipyards largely serving the Royal Navy. Tourism, buoyed by the Games, is a big, and expanding business.

But there's a downside, partly a fallout from de-industrialisation: high unemployment on large, peripheral housing estates, and an associated legacy of appalling public health, outstripping other UK and mainland European cities. Nevertheless, ambition is high.

In truth, the city is the centre of Scotland's only metropolis: 1.3 million people, a quarter of the country's population, spread across Glasgow and seven neighbouring local authorities. It is this emerging area that proved attractive to the (English) cities minister Greg Clark.

Matheson has met Clark on several occasions. The minister visited Glasgow for a recent Core Cities summit. Afterwards, this group – so far representing Manchester, Liverpool, Newcastle, Nottingham, Leeds, Birmingham, Bristol and Sheffield – declared that devolving more power to cities represented a more radical constitutional agenda "than establishing a border at Carlisle".

There's a flip side to this debate rarely heard in England. In Matheson's words, it's a misguided assumption south of the border that the constitutional settlement between the UK and Scotland delivered real devolution. On the contrary, he says it has only entrenched a centralist SNP administration which rides roughshod over local government. "They don't believe in the empowerment of cities and local democracy," he asserts. He says he finds far more in common with big English councils than with a "populist and centralising" Scottish government.

The Glasgow city deal, spread over 20 years, involves the UK government giving £500m, with the Scottish government providing a similar amount, and the eight participating authorities chipping in with £130m. Overall, it might seem a modest sum. But its significance, economically and politically, cannot be overestimated.

Matheson seems quietly confident that Scotland will say "no" on 18 September. But just suppose it voted "yes"? He says the "city deal" would be scuppered. "The rest of the UK wouldn't wear it if Scotland was not part of the UK … there's a significant threat from independence." The stakes are high.

But, for the moment, Glasgow can afford a little self-congratulation in staging the games – the result of a cost-sharing deal between the city and a previous Scottish government.