Whitehall's most senior mandarins have been told "rapid progress" is required in a range of areas if the Prime Minister's goal is to be realised.
The warning came from Martin Donnelly, the leading civil servant in the Department for Business Innovation and Skills, which is headed by Vince Cable.
It was accompanied by a list of 20 global competitiveness measures where Britain is struggling.
The measures, described as "policy priorities," show the UK ranks only 50th in the world for education in maths and science.
It is the 20th-rated nation for the speed at which planning permission can be granted, and 16th for the ease with which taxes can be paid.
Mr Donnelly wrote a letter on the issue earlier this month to Cabinet Secretary Sir Jeremy Heywood, the UK's top civil servant.
In it he said: "We now need to make rapid progress in these areas to realise the Prime Minister's ambition of being in the top five in the world."
He wrote separately to the heads of other Whitehall departments requesting "follow-up" on policy priorities where the UK is lagging behind the rest of the world. He also called for a review of the Prime Minister's pledge before the end of the year.
Britain slipped down the World Economic Forum league table of business-friendly countries from eighth to 10th this year.
After the UK's position was revealed, the Prime Minister, in a speech before the June G8 summit of world leaders, outlined his ambition to enter the top five. He declared: "We are in a battle for Britain's future."
He said he had ordered Government departments to address the weaknesses which were dragging the UK down in the world rankings.
And he set a three-year target to put Britain among the top five countries in the world - and make it number one in Europe for doing business.
Mr Cameron laid the blame for holding back the country on the UK's "debt-fuelled, unbalanced economy" and its "bloated welfare system".
Mr Donnelly's summary of 20 global competitiveness measures highlights difficulties for a number of Government departments.
The Ministry of Justice has been asked to improve on the UK's ranking as 21st in the world for enforcing contracts. The Department for Culture, Media and Sport has been alerted to the country's position in 10th place for use of the internet.
Among the most damning assessments is that directed at the Department for Transport, which has been told Britain ranks only 28th in the world for infrastructure.
The summary says this "puts us among the worst of our peer group". Other measures showed Britain was 19th in the world for starting new businesses. It was just 105th for the soundness of banks, and 55th for the number of women in the workplace.
A spokesman for the Department for Business Innovation and Skills said: "We are not going to comment on a leaked letter."
In the past the department has highlighted the UK's rise in the global competitiveness rankings from 13th in 2011. When Britain slipped from 8th to 10th, after being leapfrogged by Hong Kong and Japan in May, ministers stressed the country's score remained the same while rival nations improved.
The report found the country was losing out to other countries, such as the Netherlands and Japan.
The British Chambers of Commerce said at the time the UK was being held back by its skill shortage.
Labour also pointed out that only two other G20 countries had grown more slowly since autumn 2010 and the Tories had delivered the slowest recovery on record.