Sex is on the decline in Britain, particularly among married and cohabiting couples, according to a major study that suggests the increasingly busy lives we lead and distractions of the internet may be partly to blame.

The data comes from more than 34,000 people in the UK who took part in three waves of a large study called Natsal (national surveys of sexual attitudes and lifestyles). It shows a fall in sexual activity from 2001 to 2012 in all groups, with the steepest decline among the over-25s and those who are married or cohabiting.

The UK is not the only country where rates have slumped. Declines have been reported in Australia, Finland, Japan and the US, although in varying age groups. Researchers say one possible reason for the drop is that people no longer feel the need to exaggerate how often they have sex.

However people say they are not happy with the amount of sex they have. More than half – 51% of women and 64% of men – of Natsal respondents said in 2012 they would like to be having sex more often. That was a substantial increase from 39% and 51% respectively in 2001.

Sex is good for our health, say the authors, from the London School of Hygiene and Tropical Medicine. The NHS, they point out, “considers the evidence to be sufficiently convincing to recommend sexual activity for its health-enhancing effects, with the claim ‘Weekly sex might help fend off illness’”.

Studies have shown sex improves the immune system, lowers the heart rate and blood pressure, and reduces stress. Research suggests men and women with an active sex life are fitter and happier, have better cognitive function and longer life expectancy – although it is also true that healthier people have more sex.

The paper, published in the British Medical Journal, draws from three surveys of men and women aged 16 to 44, in 1991, 2001 and 2012. There appeared to be a moderate increase in sexual activity between the first two Natsal studies, but that was followed by a steep drop.

The researchers asked about episodes of vaginal, oral and anal sex with opposite and same-sex partners.

Fewer than half of men and women have sex at least once a week, the researchers found. Overall , the proportion of women reporting having sex 10 times or more in the past month fell from 20.6% in 2001 to 13.2% in 2012. Among the men, that figure went from 20.2% in 2001 to 14.4% in 2012.

Overall, more than 29% of both men and women in 2012 said they did not have sex in the past month, compared with 23% of women and 26% of men in 2001.

Single people who were in better physical and mental health, and those who were employed and had higher incomes, all reported having more frequent sex.

Prof Kaye Wellings and the team who carried out the research pointed to two events that coincided with the decline and could possibly be important – the introduction of the iPhone in 2007 and the global recession of 2008.

In an era of constant phone use, there may be too much going on to get around to having sex, suggested Wellings. “I can see that the boundary between the public world and private life is getting weaker. It’s porous,” she said. “You get home and continue working, or continue shopping or buy tickets – everything except for … talking. You don’t feel close when you are constantly on the phone.”

The global recession may not be such a big factor. While men with more money and better jobs reported having more sex, the decline over the years was apparent in the most and least affluent groups.

The paper says: “Most compelling among the explanations, perhaps, given the age and marital status of the people most affected, relates to the stress and ‘busyness’ of modern life, such that work, family life and leisure are constantly juggled.” Wellings spoke of a “sandwich generation” struggling to cope with so much they had little time left for sex.

But, she said, there could be other explanations. “It could be that sex is just settling down and we’re not making such a fuss about it. After the sexual revolution, there was a ‘should’ about it – you should have sex,” she said.

The decline in sex does not affect fertility rates, in spite of concern in Japan, where the birth rate has dropped. When people are trying to conceive, they have more sex, the paper says.

There is also no real evidence that health is being affected. There is no research to show any added benefit from having sex more than once a week, and there is evidence blood pressure and heart rates drop in women during touching and cuddling, regardless of the whether sex takes place.

Other research has shown the quality of sex matters more than the quantity, particularly for women, the researchers write.

But they say they are worried as to what their findings suggest about the human condition and modern life.

“The wider implications of the decline in sexual frequency are perhaps more worrying. Should frequency of sexual contact serve as a barometer for more general human connectedness then the decline might be signalling a disquieting trend. The decrease in sexual activity is interesting, unexplained and warrants further exploration,” they write.

In a commentary in the journal, Peter Leusink, a GP and sexologist from the Radboud University medical centre in Nijmegen, in the Netherlands, said the findings should encourage researchers and clinicians to start talking about sex.

The figures “conceal problems such as depression, poor physical health and relationship problems, which have all increased since the 1990s”, he writes.

“Healthcare professionals should be aware of the links between sexual health, general health and social factors, and should be alert to the possibility of sexual problems during discussions with patients.”