"Regrettably, the attitudes of a large part of society mean breastfeeding is not always encouraged," said Professor Neena Modi, who is president of the royal college.
"Support is patchy, advice is not always consistent and often overly dogmatic, support at work not always conducive to continued breastfeeding and, perhaps most worryingly, breastfeeding in public is often stigmatised."
Viv Bennett, the chief nurse at Public Health England, said: "We can all help women wherever they are. Creating a wider culture of encouragement and support will help make a mother's experience all the more positive."
Breastfeeding has many benefits for mother and child and is known to prevent infections, stave off obesity and boost IQ. Yet despite numerous "breast is best" campaigns by the UK Government and the NHS, rates have barely improved.
The royal college said that the UK Government should "ensure familiarity with breastfeeding is included as part of statutory personal, health and social education in schools".
Taught at secondary level from the age of 11, these PSHE lessons include sex education and sessions on relationships, bullying and human rights.
The royal college is also calling for "breastfeeding breaks" at work as well as designated rooms and fridges. Women should be allowed to leave to express milk into a bottle or go to a nearby crèche and feed their baby directly.
And if women choose to take breastfeeding breaks, their salaries and career should not be affected.
A survey of 1,000 mothers found many gave up early because they lacked support or worried their baby was not getting enough milk. According to the research by Mumsnet, 27 per cent of women who stopped after one day felt they did not know what they were doing. Among women who stopped after six weeks, 42 per cent were worried they were not producing enough milk and 34 per cent were just exhausted.
"There's no sense in endlessly telling women that they must breastfeed, but letting them down when they have a baby in their arms," said Justine Roberts, the website's chief executive.
"Breastfeeding is a skill, and most mothers need support when they hit a problem, especially given that they are often shattered, sore and sleep-deprived.
"The guilt, anger and sadness experienced by many mothers who switch from breastfeeding is palpable, and it's deeply unfair to leave so many feeling that they've failed."
The NHS advises women to breastfeed exclusively for six months - with no formula milk - but only 1 per cent manage this. Research by Unicef in 2012 found that modest increases in breastfeeding could save the NHS £40million a year in GP and hospital appointments.
Breastfeeding allows the mother to pass on her immunity to the baby, reducing the likelihood of coughs, colds, ear infections and allergies. It also prevents obesity in childhood as the milk has much a lower fat content than formula milk.
Breastfeeding is beneficial for the mother and helps her lose weight by burning up to 500 calories a day.
Claire Livingstone, policy adviser at the Royal College of Midwives, said: "There has been significant and reliable evidence produced over recent years to show that breastfeeding has important health advantages for both mother and baby.
"Breastfeeding is known to positively impact on mother-baby relationships as well as nurturing maternal and infant mental health."
Chris McGovern, who chairs the Campaign for Real Education, said: "Breastfeeding should not be part of the national curriculum. We've got a situation where 20 per cent of school leavers can't read or write and are essentially unemployable.
"I'm not trying to diminish the importance of breastfeeding, but schools should be focused on doing what they're supposed to do. This is just being politically correct, and schools have other priorities."
The royal college, which represents 17,500 doctors, nurses and other specialists, cautions against overbearing advice from midwives and parenting organisations that puts mothers under pressure to breastfeed. This can have the adverse effect of making women feel inadequate if they find it too difficult and then switch to formula milk.
