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Q: Almost 18 million people visited the 13 attractions in 2010-11, compared with 7 million in 2000-01.
Thursday marks the 10th anniversary of the Labour government's decision to end charges at England's national museums.
Culture Secretary Jeremy Hunt said free museums and galleries "ensure that culture is for everyone".
Entrance fees to museums, including the Victoria and Albert Museum and the Natural History Museum, both in London, were scrapped on 1 December 2001 as part of a government plan to widen access to the nation's culture and heritage.
The then Labour Culture Secretary Chris Smith, now Baron Smith of Finsbury, said at the time the move marked "an exciting new beginning for the arts and cultural life of this country".
Figures from the Department for Culture, Media and Sport (DCMS) suggest that eight of the top 10 most-visited attractions in the UK are free, government-sponsored national museums.
The British Museum, the National Gallery and Tate Britain are among museums that have never charged for entry. Tate Modern opened free from May 2000 and the Imperial War Museum North from July 2002.
Government figures show visits to museums that had previously charged for entry in London increased by 151% between 2000-01 and 2010-11. The total visitor numbers to DCMS-sponsored museums for 2010-11 was 43.8m.
In that 10-year period, visits to the National Maritime Museum were up 200% - from 800,000 to 2.4m; visits to the Natural History Museum rose by nearly 190% - from 1.6m to nearly 4.7m and visits to the Victoria & Albert Museum rose by about 180% from close to 1m to 2.6m.
Museums that still charge an entrance fee include Tate St Ives, the Imperial War Museum's HMS Belfast, the Cabinet War Rooms and the Imperial War Museum Duxford.
Full list of DCMS-sponsored museums
The DCMS says free admission attracts huge numbers of international visitors. In comparison, it says, museum charges apply at the Museum of Modern Art in New York ($25; £21), the Louvre in Paris (€10; £8.50) and the Vatican Museum in Rome (€15; £12).
According to tourism body Visit Britain, Britain's major museums and galleries earn the country £1bn a year in revenue from overseas tourists.
Mr Hunt said: "Our free museums and galleries ensure that culture is for everyone, not just the lucky few.
"I am particularly proud that we have secured the future of free museums despite the current financial climate."
Lord Smith said he had been determined to change the rising tide of charging for entry to museums.
"I had always felt that it was important to open up these storehouses of our nation's culture and history and art and science and knowledge to the widest possible range of people, and charging, in some cases quite steep admission charges, was a barrier facing very large numbers of people who might otherwise want to come," he said.
"Removing that barrier was, I thought, a really important thing to do and it has proved to be very successful."
Michael Fayle, chairman of the British Association of Friends of Museums, an independent organisation that represents friends and volunteers across the UK, said the figures showed there was "true benefit" to the public in having free museums.
But he said museums often had to foot the bill for extra visitors. For example, longer opening hours mean there is a need for extra staff.
Many museums have cafes, while others ask for a minimum donation to support the attraction.
Mr Fayle believes this is justified.
"One of the comments I heard this morning was that if you make the wider availability as free as you can at a time when central government funding isn't available, there simply has to be an alternative way of making money," he said.
However, he said charging for "blockbuster" exhibitions was a "difficult equation".
Such exhibitions bring in large numbers of visitors but the high cost of running them - and the need to recoup that money through entrance fees - means some people miss out, said Mr Fayle. He added that many visitors might find the experience diminished because of overcrowding.
"One wonders whether [holding paid-for exhibitions] is in the spirit of the free access that everyone wants to achieve," he said.
Continued access to free museums is part of the coalition government's agreement and funding to secure this was put in place in last year's Spending Review.
National museums in Scotland and Wales have been free to enter since 2001. In Northern Ireland, one of its three national museums - the Ulster Museum in Belfast - is free while the other two charge a fee.

A: Government-sponsored museums that have stopped charging since 2001 have seen combined visitor rates more than double in the past decade, figures show.
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Q: The British Medical Association said the government had failed to recognise the damaging impact long hours could have on patient care.
But NHS Employers said it was committed to talks about the safety of patients and doctors.
It said the decision to stop the talks had come as a "huge disappointment".
Under plans set out by the government in 2013, hospitals in England will have to ensure senior doctors and key diagnostic tests are available seven days a week.
NHS officials and the British Medical Association - a union that represents doctors across the UK - had been involved in negotiations about working hours for junior and senior doctors for the last 18 months.
But the British Medical Association (BMA) announced it had stopped taking part in the talks on Thursday evening.
The organisation said it was not prepared to agree to change to contracts that would risk patient safety and doctors' well-being.
Dr Paul Flynn of the BMA said: "So far the government has failed to produce any detail on how it will staff and resource a massive expansion of services in a safe and sustainable way.
"Without this detail, consultants are not prepared to sign up in the dark to proposals that could put patients at risk by forcing existing doctors to work dangerously long hours, or lead to weekday services being cut because there simply aren't enough doctors to staff them."
But Gill Bellord, of NHS Employers, said: "This is a hugely disappointing way to conclude a year and a half of serious discussions.
"All our talks with the BMA have been aimed at ensuring safer working hours for doctors in training, as well as providing them with stability of pay and agreed work schedules that take account of educational needs.
"Underpinning all of this is the essential need to deliver safe care for patients."
She added: "It is a source of personal and professional disappointment that the BMA team feel able to throw our joint progress so far out of the window and walk away from what is currently on the table."
NHS Employers said it had put forward an offer of a maximum 40-hour contract for consultants, unless extended by mutual agreement, and accelerated access to higher pay.

A: A spat between leading doctors and NHS officials over a seven-day hospital service has led to the breakdown of contract negotiations.
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Q: Businessman Andreas Christopheros, 29, was critically injured in the attack on his doorstep last December in Truro.
He suffered severe facial wounds and damage to his sight.
At Truro Crown Court, David Phillips, 48, from Hastings, East Sussex, denied causing grievous bodily harm with intent and is expected to go on trial on 8 June.

A:
A man accused of carrying out an acid attack in Cornwall has denied carrying out the assault.
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