Demand for abortions has soared among women living in countries hit by the spread of the Zika virus who fear having a baby with severe birth defects, new data shows.

In unprecedented numbers, women in Latin America are accessing the website Women on Web, which has a long history of helping those in countries where abortion is illegal to obtain pills which will terminate an early pregnancy. In Brazil, Venezuela and Ecuador the requests for help have doubled, while in other Latin American countries they have risen by a third.

Revelations about the scale of abortion demand published in the New England Journal of Medicine come as the golfer Rory McIlroy pulled out of the Olympics in Rio, citing anxiety over potential Zika infection. “I’ve come to realise that my health and my family’s health comes before anything else,” he said in a statement.

“Even though the risk of infection from the Zika virus is considered low, it is a risk nonetheless and a risk I am unwilling to take.”

The World Health Organisation is advising travellers to the Olympics to practise safe sex using condoms or abstain for eight weeks after their return, to avoid the risk of sexual transmission of the virus to a woman who is pregnant or planning to become so.

Many women living in Latin America, however, find it hard to protect themselves against the virus spread by mosquitoes and do not have the option of termination in the event of an unwanted pregnancy. It is particularly hard for those in poorer communities, living in difficult conditions where mosquitoes readily breed.

“One of the reasons for doing this study is to give a voice to women trapped in this epidemic,” said Dr Catherine Aiken, academic clinical lecturer in the department of obstetrics and gynaecology of the University of Cambridge, “and to bring to light that with all the virology, the vaccination and containment strategy and all the great things that people are doing, there is no voice for those women on the ground.”

In a supplement to the study, the researchers have published some of the emails to Women on Web which reveal their fears. “I need to do an abortion because of the great risk of infection with Zika here … Please help me. My economic situation is extremely difficult,” said one woman in Brazil.

Another in Colombia wrote: “Here Zika is a major problem and the health authorities do not help with it … I have no resources at this time and want to ask for your help because fear overwhelms me. What if the baby is born sick?” An email from a woman in Venezuela said: “We are going through a really serious situation for the economic and humanitarian crisis unleashed by Zika. There are no treatments, contraceptives nor pills to abort. I want to terminate my pregnancy but I cannot.”

Women on Web is a longstanding and well-used website which had its origins in a boat that used to moor off the shores of countries where abortion was illegal and offer help to women who arrived in dinghies. The researchers analysed data from January 2010 to March 2016 for 19 Latin American countries, comparing the numbers of requests with three countries – Chile, Poland and Uruguay – where there have been no health warnings about the dangers of Zika virus in pregnancy.

“There is a huge surge,” said Aiken. “It’s over 100% increase in demand in some of the countries we looked at – almost 110% increase in Brazil.” In those countries with no Zika outbreak, there was no such rise in demand.

The study, funded by the National Institutes of Health and the National Science Foundation, was carried out by researchers in the US and the UK. Abigail Aiken, an assistant professor at the University of Texas at Austin, said the numbers inevitably underrepresented the demand. “Accurate data on the choices pregnant women make in Latin America is hard to obtain. If anything, our approach may underestimate the impact of health warnings on requests for abortion, as many women may have used an unsafe method or visited local underground providers,” she said.

Aiken spoke of “a much, much wider problem with women who don’t have access [to the internet] and live in very poor rural areas and are in very dire straits and will be driven to less safe methods of illegal and underground abortion. We think we are looking at the tip of the iceberg.”

Women on Web helps women who are less than 10 weeks pregnant obtain an abortion, after an online consultation with a doctor. They will tell a woman where she can get the pills locally that will bring about an abortion or, if necessary, send them to her.

Women in poor areas whose pregnancy is more advanced have few options. “There is no support for those people,” said Catherine Aiken. “They can’t pay for ultrasound scans. They don’t have any choices about what they can do if there is microcephaly [a small head and brain damage]. They have no access to anyone who can help them.

“These are tragedies that are happening at the moment. Right now. Women are living in fear and it is their actuality,” she said.