All roads may lead to Rome, but few lead from Oxford to Cambridge. One of the pleasures hitherto denied me - until last weekend, at any rate - was to drive directly from Cambridge to Oxford. Forty-something roundabouts later, and after missing a couple of obscure turns on the now-you-see-it-now-you-don't A505, I did begin to wonder how the mythical land of Oxbridge manages to sustain intellectual, let alone personal, inter-relationships at all. How many Oxbridge lovers had their final bust-up beside roundabout 23 near Luton?

An old hand explained that my mistake was to look at the road map at all: "Just head for London and follow the signs." Only then did I start to understand the comment that "without London, Oxford and Cambridge are neither here nor there". And I recalled Charles Villiers Stanford, for 37 years professor of music at the University of Cambridge, who reportedly in his final professorial decades never managed to get closer to Cambridge than its railway station, where he held his supervisions.

London is everything and nothing to Britain. Everyone seems to come to, and go through, the city all the time. But is it really London: Another Country?, as this month's Radio 4 series questions? Is there a different land within the M25?

The BBC's proposition is that London has long been transmogrifying from an imperial capital into a "capital of the world". Britain may be descending the league table of nations, but London's trajectory is otherwise.

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It is a global city, as best acknowledged by it hosting the 2012 Olympics. London is a land of incredible diversity, with even more to come. The majority of primary-school students in the capital now speak a language other than English at home. But this London is also a land of re-emerging health and wealth inequalities, with wildly varying household incomes and life expectancies.

We in London's universities sell our institutions hard, but we also sell London. Choosing a university is not just about its courses or student amenities; it is also about the ambient choices of lifestyle, culture and buzz. At the recent Nafsa: Association of International Educators conference in Kansas City, I found myself selling the city somewhat along the lines of London Mayor Boris Johnson's strategy: as the financial services capital of the world; as the business capital, at least of Europe; as an international tourist hub; and as a learning, research and creativity centre of unrivalled density and variety.

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It's nice to see the growing emphasis on "smart London" in the new plans for promoting the capital to the world, because education is a London success story - and ÖйúAƬ is that story's capstone. With more than 500,000 post-secondary students (more than 100,000 of whom are international students), the academy is one of London's largest and most stable business sectors.

One reason for this educational success is the joint cause formed over the ages between London's ÖйúAƬ institutions: the inner core of the University of London, with its 19 constituent institutions; and, over the past decade, the broader and looser affiliation offered by London Higher, which has 41 institutional members. Being autonomous bodies, we all jealously guard our distinctive missions, but the need to promote, advocate, purchase, partner and share services together has never been greater.

As public funds decrease, London Higher's constituent divisions increasingly promote the DNA-in-common of its members. Study London promotes more than 30,000 accredited courses available through those institutions; School - HE links in London (Shell) builds bridges between 420 maintained secondary schools and the universities; London Medicine promotes the combined strengths of the capital's medical, dental and clinical health schools; while the new Business Development Unit cultivates the ability of ÖйúAƬ institutions to provide higher-level skills to the broader London workforce. The Podium project is helping the academy to make the most of the opportunities offered by the 2012 Olympics, while an emerging project is considering how an increasing range of services may be shared.

But the biggest challenge facing London Higher in these earliest months of coalition government is effective advocacy for ÖйúAƬ and the special needs and contributions of London's academy. As London First, our companion in employer advocacy, recognises: "London's deep global talent pool is one of the capital's key advantages and pays huge dividends in terms of investment, jobs across the UK and tax to the Exchequer."

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An emerging challenge may lie in immigration policy. The announcement on 28 June by the Home Secretary, Theresa May, of the government's intention to wind immigration back to 1990s levels - "to tens of thousands rather than hundreds of thousands" - has sent a chill wind up university spines.

While international students seem not to be affected by the policy, new university staff from outside the European Union - the mainstay of some of our departments - will be. London as "capital of the world", a country apart from the rest of the UK, risks being disproportionately affected by these "tough new limits".

The Radio 4 series describes London as "a magnet for the world's finance, culture and people". Amid growing protectionism, it needs to maintain these magnetic charms.