Thousands of American women have obtained abortion pills online in the past year, according to figures that highlight the escalating difficulty in accessing safe abortions on the ground.

Data shared with the Guardian reveals that 21,000 women requested abortion medication between March 2018 and March this year from the charity Aid Access. Between a third and a half of the women who made the requests were then sent abortion pills in the mail. The majority of the recipients live in states with hostile abortion policies.

Women who obtained pills online described desperation at being unable to access affordable medical services locally, with some saying they had considered extreme measures to end their pregnancies.

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“The reality on the ground is already so desperate,” said Rebecca Gomperts, founder of Aid Access, which provides online prescriptions for abortion pills that are dispatched to the US by mail. “If a woman cannot access a normal abortion in the US they will do anything to end their pregnancy.”

Last week, Alabama passed the first near-total abortion ban, with four other states passing bans in the early weeks of gestation, before most women know they are pregnant, threatening women’s constitutional right to abortion within America. However, the latest figures suggest that clinic closures, prohibitive financial cost and requirements for in-person abortion counselling followed by a waiting period have already caused a drastic erosion of women’s health services.

Abigail Aiken, assistant professor at the University of Texas at Austin, who analysed the Aid Access data, said: “We talk about this idea that Alabama might overturn Roe v Wade. But even now there are so many women who have a right to abortion but they cannot exercise that right.”

Abortion is legal in all 50 US states. Abortion bans in US states are an effort by campaigners to overturn Roe v Wade, a US supreme court decision which provided women the right to an abortion up to the point a foetus can live outside the womb, or roughly 24 weeks.

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Since 2006, Gomperts has run the charity Women on Web, which enables women in countries with abortion bans to terminate their pregnancies through online consultations. Doctors at the charity prescribe the two pills – mifepristone and misoprostol – that will terminate a pregnancy within the first 10 weeks. The pills are sent to women from a pharmacy based in India.

Gomperts launched the US operation, Aid Access, last year after seeing a steady increase in demand, with about 6,000 requests for abortion pills between October 2017 and August 2018. Three-quarters of requests came from states that have introduced strict anti-abortion laws, such as Alabama, Georgia and Mississippi.

The charity said it had also heard from women who said they were considering extreme measures, such as drinking alcohol or getting someone to punch them in the stomach.

In some states, anti-abortion legislation has led to a majority of clinics closing down. In Texas, there were 44 clinics in 2013, but only 19 clinics remained two years later after restrictive laws were passed reclassifying abortion centres as surgical centres, meaning they needed to have wide corridors and large operating rooms. Last year, six states were reported to have just one abortion provider in operation.

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“For people on a low income, the legal right to abortion is almost a moot point,” said Aitken.

Medical abortions before 10 weeks of pregnancy are similar to a spontaneous miscarriage and generally do not require follow up care. The first pill (mifepristone) blocks the pregnancy hormone and the second (misoprostol), taken 24 hours later, causes the uterus to contract.

Testimonies from women said to have accessed abortion pills, published by the charity in a letter last week, span a range of situations, from young women in relationships who could not afford the $900 charged by their local clinic, to mothers who did not want to have another child, to women in abusive relationships.

The US Food and Drug Administration (FDA) has issued a warning letter stating that Aid Access is violating federal law by selling “misbranded and unapproved” drugs.

• This article was amended on 24 May 2019. The figure cited for 21,000 women requesting abortion medication was for the past year, i.e. March 2018 to March 2019, not the past six months, October 2018 to March this year as an earlier version said