They said: 'This emphasises the opportunity for earlier intervention in primary care to reduce suicide risk'.
Referrals to mental health services within 12 months of self-harming were 23 percent less likely for children in the poorest areas, even though the rates of self-harm were higher in these areas.
For girls aged 13 to 16 the rate rose from 45.9 per 10,000 in 2011 to 77.0 per 10,000 in 2014.
The study found that, between 2011 and 2014, there was a 68 per cent increase in reports of self-harm among girls aged 13 to 16.
In about 55% cases of self-harm in the United Kingdom, there was no referral to mental health services recorded.
While Kapur says it is unclear what is behind the apparent rise, previous research has suggested a growing number of young women are experiencing mental health problems, with contributing factors including worries about appearance.
Based on data from 674 GP practices across the United Kingdom, the findings reveal that annually between 2001 and 2014, on average 37.4 girls per 10,000 and just over 12 boys per 10,000 reported their first episode of self-harm.
The researchers also found that children and teens who self-harmed had a nine times increased risk of death from non-natural causes.
They were also 17 times more likely to die by suicide. Of course such technologies can be helpful and facilitate access to care but there is also a suggestion that extreme "connectedness' could have detrimental effects", the authors continue.
Nav Kapur, professor of Psychiatry and Population Health at the University of Manchester, said: "We can't really explain this possible rapid increase in self-harm among girls". It could reflect better awareness or recording of self-harm in primary care.
"It is possible that the higher rates in this study reflect better identification, and more young people seeking treatment from Global Positioning System and/or higher severity of the self-harming behaviours compared to previous years", she said.
There is some evidence indicating that common mental health disorders are becoming more common within this age group.
An NSPCC spokesman said: "These heartbreaking figures are sadly unsurprising because Childline hears from so many young people who hurt themselves".
Experts acknowledge self-harm as the biggest risk factor for subsequent suicide, with suicide now the second most common cause of death in the under 25s worldwide.
"Self harm can often be an expression of a deeper problem which is why early intervention services to support these children are vital".
"Talking treatments such as cognitive behavioral therapy help prevent repetition of self-harm in adults", he said. "Without this, the consequences really can be a matter of life or death".