Britain doesn't have a second city, according to a BBC documentary that’s captured the attention of Birmingham’s political class.

Neither Birmingham nor Manchester deserve the epithet, according to BBC journalist Evan Davis, whose two-part series Mind the Gap looked at the relationship between London and the rest of the country.

The key issue for him is size. London’s success is a result of packing so many people into the same place, according to Mr Davis. This is a phenomena known to economists as agglomeration.

And the trouble with Birmingham, or Greater Manchester, is that they’re just too small to follow London’s example.

The capital has a population of just under 10 million, while Greater Manchester has 2.5 million and the West Midlands metropolitan boroughs have 2.4 million between them.

His answer is to create a new city in the north with a combined population of roughly half London’s – taking in Manchester, Leeds and Liverpool, as well as their surrounding areas.

This doesn’t have to mean a continuous built-up area, concreting over the entire north of England. It could involve improving transport links between the major urban areas so that nipping between Leeds and Liverpool is as easy as journeying across London.

It might be tempting to see the documentary as the latest contribution to the debate about whether Manchester or Birmingham is the “second city”, but that wasn’t really the topic Mr Davis was addressing.

And I’m not sure whether his proposal for a mega city in the north was entirely serious, or whether it was meant more as an illustration of what would have to happen if the UK really did hope to create a new city in the same league as London.

The real point is this: London is something different to the other cities of the UK. Some people argue that it’s not a city at all, although I’m not sure what we could call it instead. But with 10 million people, and a global profile and influence matched only by New York, London is a different beast to Birmingham, Manchester or Leeds.

There’s no point trying to compete with it. The goal for the West Midlands has to be find a way of ensuring London can be used as a national asset to benefit the entire country – not to become a smaller version of the capital.

Once upon a time, this might have been regarded as heretical thoughts. But increasingly, Birmingham’s MPs, council leaders and business figures have taken the view that trying to fight London is pointless.

And a second heretical thought follows logically from this – that the whole idea of a “second city” is meaningless.

If Manchester wants to define itself as being second behind London then they can knock themselves out.

What Birmingham needs to do is to define itself as a great place to do business, to collaborate with and to visit – across the UK and across the world.

Constantly inviting comparisons between yourself and London isn’t a particularly helpful way of doing that (but boasting that London’s attractions are less than an hour away on the train might help).

And our politicians are indeed doing their best to promote the city. Hence, Birmingham Council leader Sir Albert Bore has been leading a delegation to property show MIPIM (apparently it stands for le marché international des professionnels de l’immobilier) in Cannes, while his predecessor in the role, Mike Whitby, was on the plane to China on a regular basis.

But there’s one challenge our leaders are only beginning to face up to, and that’s the fact that it makes no sense to try to promote Birmingham in isolation from the rest of the West Midlands.

Here, I mean the metropolitan area known as the West Midlands – Birmingham, the Black Country, Solihull and Coventry – not the wider “West Midlands region” which includes Stoke on Trent and stretches west to the border with Wales.

It would be ridiculous for Sir Albert or someone like Andy Street, chair of the Greater Birmingham Local Enterprise Partnership, to avoid mentioning the Black Country if, for example, they are discussing the region’s skills base and expertise in engineering with a potential investor.

And it would be just as foolish for the Black Country to refuse to work with Birmingham.

What’s more, Ministers have made it clear they are far more willing to devolve powers to a combined “city region” authority than fragmented councils – and rightly so.

Consider, for example, business rates. Ministers might allow councils to cut rates in areas where they want to promote economic development, but the region will only benefit if councils use this power to attract investment from elsewhere rather than to compete with their immediate neighbour.

It’s debatable why West Midland councils have found it hard to co-operate in the past. But, miracle of miracles, they seem finally to have got the message that they need to work together.