Forecasters have good news for those fearing that Britain faces a long, slow decline into economic mediocrity: the UK will still stand tall among the world's biggest economies in 2030, having overtaken France and even made progress on closing the gap with Germany.

Only India will leapfrog the UK on the rich list of nations, according to the report by PricewaterhouseCoopers (PwC), as the previously fast-growing countries Russia and Brazil struggle to make ground on the global league table.

According to the report, the youthful vigour of the UK economy, with its high birthrate and flexible labour market, will contrast markedly with the ageing populations of mainland Europe.

Ignoring the potential for Scotland to spoil the party by voting to separate in September, the report forecasts that Britain will remain "a significant member of the global economic A-list".

Barret Kupelian, economist at PwC and co-author of the study, said the UK economy had regained its dynamism in recent years in contrast to France.

"The UK should also narrow the GDP gap with Germany over time, although this is projected to be driven mostly by the UK's more favourable demographics, with a less rapidly ageing population and strong labour force participation rates."

In the longer run other emerging markets might overtake the UK, he said, but only India would manage this before 2030, based on GDP at market exchange rates.

François Hollande, already under pressure for presiding over a weakening French economy, is unlikely to welcome a prediction that things will go from bad to worse as his country slips from fifth place to sixth by 2020 and to eighth by 2030 in the GDP rankings.

Only a couple of years ago there were forecasts that Britain would rapidly become a second-class economic power and would need to defer to the BRIC countries of Brazil, Russia, India and China in the near future.

China has ranked above Japan for a decade as the world's second-biggest economy. By some calculations Brazil leapfrogged the UK in 2012, with Russia and India close behind.

Britain's fall was partly related to the costs of the banking crisis and the recession that followed, coupled with a sharp decline in the exchange rate, which knocked about a quarter off the country's value in relation to its main rivals.

But since the beginning of last year the economy has recovered all the lost ground from the recession and banks have begun lending again. The pound has bounced back from about $1.40 in 2009 to $1.71 today.

Brazil, by contrast, has suffered a rocky couple of years that have slowed GDP growth and pushed down the value of the real. Russia will close the gap on the top eight, but its reliance on the oil and gas industry for growth and its rapidly ageing population will prevent it jumping up the table as quickly as previously thought.

Only India will move ahead of the UK by 2030, though it will be sharing a projected GDP of $6.1tn among more than 1.5 billion people, only half as much again as the UK's predicted output of $4tn, produced by a population less than a 20th the size.

India will surpass China as the world's most populous country by 2050, according to research by the Pew Research Centre, by which time its population is expected to have increased by 400 million to 1.6 billion.

China, which is projected to add just 25 million people by 2050, is widely regarded as the only major country that is going to grow old before it gets rich. It will remain the world's second-largest economy behind the US, but without the necessary numbers of young people or immigrants to outstrip its western competitor.

PwC said policymakers in London should guard against taking too much comfort from the report. The UK remains below average in the report's "social progress and cohesion" category in the Escape Index, which ranks each country's performance across 20 economic, social, technological, environmental and political indicators.

On this basis the UK scores only fifth out of the G7 economies in 2013, ahead of France and Italy but behind Germany, the US, Japan and Canada.

This compareswith the country's third place in 2000 and 2007, when inequality was less marked and figures showed the population spending more time in education on average than now.

John Hawksworth, chief economist at PwC, said: "The UK has noted strengths in areas such as political, legal and regulatory institutions, including ease of doing business, and communications technology. The UK also scores relatively well on some economic variables such as unemployment , and its relative growth and inflation performance also improved in 2013, which looks set to continue in 2014.

"But the UK lags behind its peers in areas related to education, investment, trade deficits and income inequality. So the UK has clear strengths to build on, but also some underlying weaknesses to address even given its recent relatively strong economic recovery."

But spare a thought for Italy. The increasing numbers of old people applying to Rome's creaking pension system mean the country faces dropping out of the top 10 for the first time in more than 40 years.