Giving birth at home or in a midwife-led birth centre is just as safe as going into hospital for women who already have a child, but there is a slight extra risk of problems for the babies of first-time mothers who opt to stay at home, according to a study of more than 64,500 births in England.

Women with low-risk pregnancies should have the right to choose where they want to give birth, conclude the authors of the research, set up to answer the fraught question of the relative safety of hospitals, birth centres and home.

Professor Peter Brocklehurst of the University of Oxford and colleagues in the Birthplace in England Collaborative group found that adverse outcomes for the baby – including stillbirth, death soon after birth and oxygen deprivation whichthat could cause brain damage – were rare in women who had low-risk pregnancies. Overall, they happened in 4.3 births per 1,000 and there were no significant differences between hospital obstetric units and elsewhere.

There was, however, an increase in the risk of an adverse outcome for babies of first-time mothers at home – 9.3 per 1,000 births, compared with 5.3 in hospital and 4.5 in a dedicated birth centre. Taking out those women who had any sort of complication at the start of labour, the gap was slightly bigger because hospital outcomes were better: 9.5 per 1,000 at home compared with 3.5 in hospital compared with 9.5 per 1000 at home, which is an increase of nearly 3%.

The slightly worse outcomes at home for first-timers are unexplained. "I don't know why. We don't know which aspects of the care or the site contributed to this," said Brocklehurst. It could be to do with the sort of women who chose home birth, who tended to be white, slightly older, better educated and live in more affluent areas, the midwife's experience, problems in transferring to hospital in an emergency or something else entirely. More work would be needed to establish what was happening.

First-time mothers who started at home were much more likely to be transferred to hospital – 45% were moved, compared with less than 12% of women who had given birth before. Usually this was because labour was not progressing or an epidural was needed.

The risks for the baby dropped dramatically for women having their second or subsequent child, to 2.3 per 1,000 at home, 2.7 in a midwifery unit and 3.3 in hospital.

The study, published in the British Medical Journal, found the experience for the woman was very different between hospital and other settings. Those who planned to give birth at home or in a birth centre and at least started their care there were far less likely to have interventions such as caesarean sections, epidurals for pain relief and forceps deliveries. More than 11% of women whose care began in hospital had a caesarean, compared with 2.8% of those who began at home. In hospital, 6.8% of deliveries were by forceps compared with 2.1% at home.

The authors say their findings have implications for planning NHS maternity care. Only 4% of women give birth at home and midwife-led birth centres are available in only half the areas of England.

"These results will enable women and their partners to have informed discussions with health professionals in relation to clinical outcomes and planned place of birth," say the authors. "For policy makers, the results are important to inform decisions about service provision and commissioning."

The National Childbirth Trust, a charity that supports parents, said pregnant women and their partners should have all options available.

"Different settings appeal to different people, and if a woman feels comfortable and secure in the environment she and her partner have chosen, she is likely to feel more in control during birth," said spokeswoman Mary Newburn. "For women who are healthy and have a straightforward pregnancy, the options to give birth at a midwifery unit or at home have much to recommend them.

"For low-risk women in first and subsequent pregnancies, care in a midwifery unit is safe for them and their babies, and leads to more straightforward births without medical interventions such as an emergency caesarean."

Parents should have the different risks and benefits explained to them by midwives and other professionals during the pregnancy, so that they could make an informed decision. "The new evidence provided by Birthplace would support more birth centres being opened, creating positive choices for many more women," she said.