One in four women who had an abortion in 2016 were using the most reliable methods of contraception, says the British Pregnancy Advisory Service.
More than 14,000 women, who were treated at BPAS clinics, became pregnant despite using the pill or a long-acting contraceptive.
They often spotted their pregnancy late because they hadn't expected their contraception to fail.
No method of contraception can ever be 100% effective.
But long-acting reversible methods are said to have a very low failure rate (99% effective).
Oral contraceptive pills are by far the most popular way of protecting against unplanned pregnancy among women, but long-acting methods – known as Larcs – are catching up.
They include contraceptive injections, implants and intra-uterine devices (IUDs) or systems (IUSs).
Contraceptive pills are estimated to be 91% effective while condoms are 82% effective when used typically.
However, BPAS says unplanned pregnancies can occur if the method is not inserted properly, or if it moves or falls out.
It also says hormonal contraception, such as the pill or patch, can mask the symptoms of pregnancy because they may cause light or irregular periods.
This may be why women using these methods have abortions at a later stage than other women.
BPAS said that in 2015, more than 5% of women having abortions past 20 weeks were using Larcs, compared to around 3% of those having one at less than 19 weeks.
The legal limit for abortions is 24 weeks in England, Wales and Scotland. Women in Northern Ireland are now able to get free abortions in England.
Ann Furedi, chief executive of BPAS, said: Our data shows that women cannot control their fertility through contraception alone, even when they are using some of the most effective methods.
"Family planning is contraception and abortion.
"Abortion is birth control that women need when their regular method lets them down."
Out of 60,000 women who had an abortion at BPAS clinics last year, more than half were using at least one form of contraception.
The total number of abortions in England and Wales has been around 185,500 during each of the last few years.
Every year, nine in every 100 women using the pill, six in every 100 using the injection and one in every 100 using the IUD become pregnant.
Abortions are only allowed in Northern Ireland if a woman's life is at risk or there is a permanent or serious risk to her physical or mental health.
The sexual health charity FPA said people did not always use contraception consistently or correctly.
It also said some of the most effective methods of contraception were not always made as available as they should be.
"In a survey of GPs, we found that one-fifth don't offer the intrauterine device (IUD), and almost a quarter said they don't offer the contraceptive implant," the FPA said.
GPs told the FPA that this was partly because of a lack of training qualifications and a lack of funding.
But NICE (National Institute for Health and Care Excellence) guidance suggests that long-acting methods of contraception can reduce unintended pregnancy and be cost-effective for the NHS. (BBC)