In London, there are more cranes on the skyline than in the rest of the country put together. Evidence is growing that a recovery is under way, but there are now fears that only the south-east is benefiting, leaving the nation more divided

House prices in London's swankiest districts are clocking up a rise of £27 every hour of the day and night. It sounds like a statistic from the dizzy days before the Great Recession, when ostentatious consumption was in, "banker" had yet to become a dirty word, and the capital prided itself on providing a haven for the world's super-rich. But it's the story today in the prime postcodes, which are basking in a spring recovery yet to be felt in the rest of Britain.

Analysis of official data by London Central Portfolio, which helps investors to buy in the capital, shows that the cost of a property in one of central London's "prime" areas, such as Knightsbridge or Kensington and Chelsea, has jumped a whopping 25% in the last year to an average of £1,186,817.

London's skyline bristles with giant cranes as the construction industry cranks back into life, while deep beneath the capital hundreds of workers are digging 42km of tunnels for the vast Crossrail project, which will connect the heart of the city from east to west, in Europe's largest construction project.

On the south bank of the Thames, near London Bridge, there is no shortage of visitors willing to pay the £24.95 entry fee to admire the spectacular views of the city from the top of the Shard, the giant Renzo Piano glass-and-steel pinnacle, financed with Qatari cash, which opened in February.

Just around the corner in Borough Market, each Saturday morning brings a flock of foodie shoppers to stock up on artisan cheeses, hand-dived scallops and craft beers. Across the river in the City, the vast London outpost of US restaurant chain Sushisamba high up in the Heron Tower – another recent addition to the increasingly crowded skyline – is booked up, with well-heeled diners keen to sample its "unique blend of Japanese, Brazilian and Peruvian cuisine culture, music and striking design". At times London in 2013 feels more akin to Manhattan than, say, Manchester.

There is nothing remotely New York about the waterfront at Brough, in the East Riding of Yorkshire. No cranes, no bustle of industry. Just the muddy Humber river sweeping past a vista of mudflats, coastal lagoons and saltmarshes. A major centre for aircraft manufacture since 1916, where more than 80 models of plane were built over the years, this is the kind of place that might hope to be swept up in a 21st-century industrial renaissance.

But while BAE Systems still has a presence only yards from the waterfront, the company is no longer the force it used to be here. At the height of the recession, a fall in orders forced BAE to announce the potential loss of 899 jobs.

Eighteen months on, that figure has mercifully been limited to "an anticipated 30 compulsory redundancies," as staff have been switched to other sites or found jobs with new employers in now redundant BAE premises. These days the town – population 7,000 and rising – is less a base for advanced aeronautical engineering and more a genteel dormitory for the likes of Hull, Scunthorpe, Grimsby and Leeds.

"The people doing the best are those who catch the train out of here to London every morning," says David Funnell, who proudly sells "Yorkshire ground" coffee outside Brough station. "You'll see them park their top-of-the-range Lexuses, Mercs and Range Rovers and head off to the south. What they're leaving behind is part of the north that's increasingly being left behind by the government."

Frazer Ulrick, a specialist in business restructuring with Begbies Traynor, had just emerged with a bag of groceries from Morrisons. "The south is definitely more affluent," he says. "But then, they have to pay higher house prices and so things balance out. Overall, I feel I'm better off where I am. We have a nice house and Brough is a great place to bring up children."

Ulrick, 33, and his wife Emma, 31, bought their three-storey terrace home in "New Brough" in 2008. "We paid £150,000 for it, and because it's still probably worth that, our next house is not getting further away," he says. "If we were in London, we'd need to be finding the extra £27 an hour to make that same move."

Five years after the crash, there is finally talk of a (modest) economic upturn. The National Institute of Economic and Social Research has estimated that the economy expanded by a healthy 0.8% in the three months to April.

But where is the growth happening? And who is benefiting? The evidence suggests that an unbalanced recovery is in prospect, during which London and its environs will effortlessly pull further away from the rest of the country. Welcome to two-speed Britain.

In the capital, for anyone looking for economic green shoots, there are anecdotes aplenty – packed restaurants, high-spending shoppers, ambitious building projects.

"There's a lot of private sector money coming into London; there's a phenomenal amount happening," says Gerard Lyons, chief economic adviser to the mayor of London, Boris Johnson. "London is leading the recovery."

But when the coalition government came to power in 2010, George Osborne hoped to build an economic model that no longer depended on the spendthrift habits of a few hundred thousand impossibly wealthy bankers and resident Russian oligarchs. Instead, he pledged to lead a "march of the makers", rebalancing Britain's growth model away from debt-fuelled spending towards industry. In turn, that would help to spread the benefits of growth beyond the capital.

Yet while the green shoots are showing in London, it's a different story elsewhere. "If you look at Glasgow city centre at the moment, there are no cranes to be seen," says Allan Lapsley, a partner at property advisers Speirs Gumley. "If I go to London there is just a different feel, like there is no recession. There is a buzz that hasn't gone away. Whereas at this end we've had our heads in our hands for the last two or three years."

The huge public spending cuts of the last three years have made a difficult economic situation in the north and other regions even worse. David Tinsley, UK economist at BNP Paribas, says: "It has been an unbalanced recovery, and typically unbalanced recoveries in the UK tend to favour the south as they tend to be consumer- and housing market-led."

It is, of course, in the property market where the contrast between London and the financial health of the rest of the country is most stark.

Property developer Christian Candy is working on plans for a lavish development in the grounds of the Royal Hospital, Chelsea, where prices are expected to reach £200m. Meanwhile, houses in Wales are changing hands for a few thousand –the cost of a single designer lampshade in one of London's luxury pads.

Luxury property agents Knight Frank say that London's market is boosted by rich overseas buyers who see a house in the capital as a safe haven investment. They report that foreign buyers accounted for 52% of all prime central London sales worth more than £2m over the past year.

"The increasingly volatile global economy has only served to fuel demand among global investors," says Liam Bailey, Knight Frank's global head of residential research.

"The London market has really outperformed over the last four years, and over the past 12 to 18 months it has become more noticeable. The eurozone crisis undermines confidence in the UK and hurts the housing market but it is positive for London because eurozone investors look to London as somewhere to buy."

London ranks top in the world – ahead of Tokyo and New York – for the number of multi-millionaires, although it also has some of the worst child poverty rates in the UK. The capital has 4,224 multi-millionaires – classed as individuals with net assets of $30m (£19m) or more excluding their primary residences, according to analysts Wealth Insight. It puts the number of dollar millionaires at 281,000 or, in other words, a staggering one in 29 Londoners.

These are people Johnson is eager to hang on to, as he stresses the tax revenue that is being garnered from the capital's financial services and its high-earning employees. But if London begins to pull yet further away from the rest of the UK as recovery takes root, resentment may grow that the crucible of the financial crisis which plunged the economy into the deepest recession in a generation is – yet again – taking the lion's share of the benefits of growth.

Professor Karel Williams, from the Centre for Research and Socio-Economic Change group of academic researchers, says that the divergence between the fortunes of London and the rest of the country is the result of deep-seated flaws in the UK's economic model.

"We're seeing a fragmentation of the social settlement," he comments. "This country is a pleasant, prosperous place for some social groups, but it's a depressed hole of shuttered shops for others. What we're heading for is a two-speed UK."

He argues that the chasm between the cost of a home in the capital and in the rest of the country exacerbates the problem: "The ex-industrial working class are marooned by the lack of cheap housing. For somebody who's lost a council job in the north of England to come down to London with a family – how would they live?"

Governments have wrestled for decades with the challenge of regenerating the northern towns that were the powerhouses of the industrial revolution.

Ed Cox, director of the thinktank IPPR North, says that, without rekindling growth outside the capital, UK plc will remain stuck in the doldrums: "If you focus exclusively on jobs and growth in London and the south-east, it will be very difficult to turn the economy around."

That idea was echoed in Lord Heseltine's recent report, No Stone Unturned. He called for £49bn of Whitehall funding to be allocated to local enterprise partnerships – the bodies set up by the coalition to replace Labour's regional development agencies – to spend on transforming their local economies. But with ministers reluctant to cede control over large chunks of their budgets, the amount eventually handed down to local level looks likely to be a tiny fraction of that.

Cox says the enterprise partnerships are "slowly starting to get their act together and the government is slowly realising that they need a degree of capacity". Enterprise partnerships are an integral part of the "city deals", under which eight "city regions", including Birmingham, Newcastle and Sheffield, were recently handed new powers over economic development. Cox points to bioscience and engineering as industries in which the north has great strengths. "It's not all about metal-bashing," he says.

The latest official trade figures, published on Friday, showed a strong rise in exports, boosting hopes that a march of the makers may finally be about to get under way, helped by a cheaper pound.

But back in Brough, at his commuter-friendly coffee stall, Funnell is sceptical that the coalition has a convincing plan for spreading the benefits of growth beyond the capital.

"We're proud folk in Yorkshire, but we're getting increasingly fed up with the government," he says. "They feel that Cameron's Eton and Harrow set are making policies for Londoners and don't care about the rest of the country. In their minds, we're all 'flat caps and ferrets'."