Increased life expectancy and low birth rates mean that by 2030 there will be fewer than three people aged between 15 and 64 for every pensioner living in the region.

The impact will be most striking in North Yorkshire, where the number of people aged over 85 – those most likely to require round-the-clock care – is projected to rise by 65 per cent between 2001 and 2020.

The demand for care services will be so great that, unless it changes its procedures, North Yorkshire Council will need an extra £43m a year to cope.

Other councils and health trusts will also have to make savings to prepare for the demographic shift, which is likely to lead to large rises in dementia, cancer, heart disease and stroke.

The number of people with severe dementia could be as high as one in four in some areas.

North Yorkshire Council's corp-orate director for adult and community services, Derek Law, said: "There is no doubt that, with the increase in numbers of older people coming through the system, what comes from Government support grants and local taxation hasn't been enough to sustain the enormous outlay.

"We know we have got a deficit and if we didn't do things more efficiently we wouldn't survive the next three or four years. It's a demographic time bomb."

Tony Warnes, professor at the Sheffield Institute for Studies on Ageing, said health service managers had to keep "a very close eye on demography and the age structure".

"There is significant internal migration going on in the Yorkshire region, with a lot of late middle-aged and older people moving out of urban areas into North Yorkshire and East Yorkshire," he said.

"There are signs of a great disparity in rural areas, particularly North Yorkshire, where the population is getting older faster than in West Yorkshire and South Yorkshire. That raises big opportunities and challenges.

"A lot of those people moving out are owner-occupiers who are bringing money and spending power into rural areas and are supporting quite prosperous
little towns.

"But there are, of course, a number of issues in terms of whether these people could be getting themselves into situations that are less convenient.

"These could include transport if, for example, people have to give up their car when they live somewhere with no bus service, and there are issues for local health services and social services as well."

Population figures published in a report by research agency Yorkshire Futures show that there were 4.1 people of working age for every person aged 65 or over in Yorkshire in 2006.

But that ratio is expected to fall to 2.7 by 2030 as the population ages significantly and could drop to as low as 1.7 in areas such as Ryedale, Hambleton and Craven and even 1.6 in Scarborough.

Council chiefs expect 155,300 over-65s to be living in North Yorkshire in 2020 – up 50 per cent on 2001.

About one in four people aged over 85 will have a significant degree of dementia, with cases set to increase by 54 per cent.

But the number of people aged 20 to 40 is expected to fall, which could mean a shortage of carers.

North Yorkshire and York Primary Care Trust has announced an overhaul of how it spends its money, based on statistics about the region's ageing population.

Its director of public health, Peter Brambleby, said: "We've been looking at school rolls and electoral rolls, trying to get a handle on who we have here; we get a different amount of money for different age groups."

David Cameron revealed to the Yorkshire Post that the Tories were considering an American scheme whereby pensioners would not have to sell their homes to pay for residential care. If they saved enough to pay for one or two years' care the rest of the costs would be covered.