The population of England and Wales increased by 3.7 million over the past decade – the biggest rise since national records began in 1801, according to initial results from last year's census.

Buoyed by increased life expectancy, sustained immigration and robust fertility levels, the number of residents jumped 7.1% from 52.4 million in 2001 to 56.1 million in 2011 – the highest growth rate of the past century, said the Office of National Statistics (ONS). The population of Northern Ireland, according to results released separately, was 1.8 million – up 7%.

In contrast to the 2001 population survey – when populations in the north-east and north-west of England declined – all regions of England and Wales grew in size during the last 10 years of record growth. London showed the biggest rise, gaining more than 850,000 residents and bringing its population to more than 8 million, while the south-east and east of England also boomed. Of all local authorities, Newham and Tower Hamlets had the highest rates of growth.

According to an estimate by Glen Watson, director of the 2011 census, the new figures could take Britain's population above 63 million. The true figure will not be known until Scotland releases its results later in the year.

Prompting renewed criticism of immigration policy from MigrationWatch UK, Watson said more than half the increase in England and Wales, representing just over 2 million people, was "due to the effects of net migration". But the remaining 1.6 million was due to longer life expectancy and an increase in fertility among women born in Britain.

He admitted that the census had uncovered 480,000 more people than had been expected in previous ONS forecasts. "Clearly there's been an awful lot of change in the last decade," he said.

The growth spurt reflected in the first tranche of results from the census, which was carried out in March last year, makes England the fifth fastest growing country in the European Union, and Wales the 11th. The number of people living in England grew by 7% to 53 million. Wales's population increased 5% to just over 3 million.

As the post-war baby-boom generation reaches retirement, the 2011 statistics also paint an unprecedented portrait of an ageing population. One in six people in England and Wales is over 65, with about a dozen local authorities – many of them coastal, such as east Devon and west Dorset – boasting a pensioner population of more than a quarter. Among over-90s, said Watson, the population growth was particularly vigorous: an age group which totalled 13,000 in 1911 now numbers 430,000.

The under-fives have swollen by 400,000 since 2001 to 3.5 million. "That is partly to do with the children of migrants but also partly to do with increasing fertility of UK-born women," said Watson. Also giving a glimmer of hope to those who predict demographic doom is a 1 million rise in the number of people in their 20s and early 30s, which Watson said was attributable to migration.

The growth in population has led to an increase in density in some parts of England, with an average 371 residents per square kilometre compared with 347 in 2001. The picture, however, is mixed. While in parts of London such as Islington or Kensington and Chelsea, there are more than 13,000 people per square kilometre, but 215 local authorities have fewer than 1,000. Anyone wanting real peace and quiet should consider moving to Eden in Cumbria, where there are 25 people per square kilometre.

In a very few parts – 17 local authorities including Barrow-in-Furness and Sunderland – the population has bucked the general trend and decreased. "Almost half the local authorities with a declining population were in the north-west, and a further four were in the north-east," said the ONS in a written briefing. "Most of these areas are urban, and several have experienced decline in traditional manufacturing industries."

Just about the only feature of the demographic picture that has not changed since 2001 is the average household size. But behind the static appearance lies a host of competing influences, said Watson, including a growing trend for young people to move back in with their parents when they finish university. "With people living longer and with some families breaking up and more people living alone, you might expect to see a decrease in household size," he said. "But of course that's counterbalanced by a couple of other factors, including the increase in the number of children and also the tendency for children to return home after higher education and live with their parents for a while."

The ONS hailed the 2011 census as a "great success", but added that about one in 20 people had failed to fill in forms. It put the unexpected 480,000 people down to an assumed shortfall in the 2001 census, which was carried forward in population estimates throughout the decade, and partly to an underestimation of net international migration over the decade, which would represent 267,000 of the 480,000.

One local authority, Westminster city council claimed the census had again underestimated its population, putting its funding at risk because grants from central government are based on population estimates. "We have serious concerns about today's census figures, which at 219,400 represents a 9% reduction from the previous estimate in 2010," said Melvyn Caplan, a spokesman for Westminster city council, which claims the 2001 results under-estimated its population by 26%. "We are really disappointed to be facing a similar situation … we need to look at the figures more closely and ask the ONS to open up its process to us so we can figure out what has happened."

Watson said he would be happy to talk with the council about the results but insisted they were "plausible". "For the 2011 census we went to great lengths to try and make sure that the population in London was properly counted … we've satisfied ourselves that all of our figures are plausible and stack up against these other sources," he said.

The ONS said comparisons made with 2001 in the results did not refer to that year's census, with which it admits there are "known issues". The 2001 figures are drawn from corrected data.