Many are now seeing three figures
The Office for National Statistics says there are now 9,000 "centenarians" - a 90-fold increase since 1911.
Estimates suggest this will carry on rising to 40,000 by 2031.
The rapid increase in the number of very elderly people began in the 1950s and is due to improvements in housing, healthcare, nutrition and sanitation.
The proportion of the population above the age of 70 has been rising steadily, and is expected to rise further.
The over-90s are now the fastest growing age group.
Experts say this is likely to place a far greater burden on the health service, as the costs of catering for diseases of the elderly such as cancer and dementia rise too.
The same increases have been happening in other industrialised countries, the ONS says.
There used to be proportionately more female to male centenarians - seven women for every man.
However this ratio is now beginning to fall as survival to this age becomes more common.
Greater male effect
Recent improvements in death rates have been greater for men than for women.
Help the Aged
Although the rate at which the number of centenarians increased actually fell between 1981 and 2000, this reflects a slowing down in the birth rate a century earlier, rather than a worsening of the lifestyle and living conditions which contribute to long life.
There were only 100 centenarians in 1911 - up to 1940, the annual increase was 1.9%, rising to approximately 6% between 1941 and the 1990s, 4.5% during the 1990s and 5.8% since 2002.
The ONS expects that the number of over-100s in England and Wales will rise an average of 6% per year, quadrupling the current number by the 2030s.
Dr Lorna Layward, from Help the Aged, said: "It's hard to know whether these extra years are providing extra years of good health.
"Hopefully, with better medical provision, these extra years can be happy and healthy."
Emma Soames, the editor of Saga Magazine, said: "The government has got to get its act together, because the care services in this country are really not fit for purpose at the moment.
"We have a whole generation in their 50s and 60s who are looking after elderly relatives."
Gordon Lishman, director general of Age Concern, said: "Demographic change presents a number of opportunities and challenges to public services and public spending.
"For example, most people living in care homes are over the age of 85. As the number of people over the age of 90 increases, so will the need for care home spaces.
"All too often we are failing to respond adequately to the changing demographic challenge facing the UK."