The number of women contacting a charity that helps people in Ireland seek abortions in Britain is set to double for the third year in a row, according to new figures released ahead of major demonstrations in Belfast on Saturday by pro-choice and anti-abortion campaigners.

The London-based Abortion Support Network (ASN) said that tough economic conditions were making the process of accessing abortion even harder for poorer Irish women, and that official Whitehall data suggesting an overall decline masked the number of women who disguised their background in official NHS forms or took advantage of cheap flights to have abortions further afield.

The statistics come at a fraught time in the ongoing debate over abortion in Ireland, where the procedure is illegal unless the life of the woman is in danger. Pro-choice campaigners from the Irish Republic and Northern Ireland, where abortion is also restricted, are staging a major rally in Belfast to press for reform and protest against a controversial campaign by anti-abortion activists who are taking part in a separate Rally for Life. The campaign involved billboards showing either a picture of a woman or her foetus symbolically torn in half above the tagline: "Abortion tears her life apart. There's always a better answer."

In April, the Irish government rejected a private member's bill seeking to provide limited access to abortion. The government said the Irish parliament should await the report of an expert group, which was appointed after the European court of human rights ruled that the Irish state had failed to implement existing rights to lawful abortion where a mother's life is at risk.

The campaign to loosen the country's abortion ban is focusing on the right of women whose unborn babies have been diagnosed with serious conditions and are unlikely to live.

Three women have told the Guardian about their experience of being told their babies would die and that they must continue with the pregnancy, potentially to full term. All three travelled to England for abortions, with one describing having to leave Ireland for the procedure as "barbaric". They are calling for human rights organisations, feminist groups and parliamentarians across the world to urge the Fine Gael-Labour coalition to reform the law.

Figures released in May by the Department of Health (DoH) showed the numbers of women from the Republic of Ireland travelling to England and Wales for abortions fell by 7% last year, but ASN, which provides economic support and accommodation for women seeking abortion in the UK, said that Irish women in financial distress were now seeking its help in greater numbers.

"The continued economic crisis is making it even more of a struggle for women and families to keep their heads above water and Ireland's severe abortion restrictions make it even harder for this group," said ASN's director, Mara Clarke.

The decline shown in DoH figures has been linked to improved access to sexual health education and access to contraception, as well as Irish women giving UK addresses or choosing to travel to Spain and the Netherlands for terminations. The ASN said the number of calls it had received from women in the first six months of this year was 183, compared with 251 throughout 2011 and 89 in 2010.

The three women campaigning for change – Arlette Lyons, Ruth Bowie and Amanda Mellet – describe being compelled to travel away from their country, family and friends to terminate doomed pregnancies as "bizarre, barbaric and absolutely cruel".

Bowie, a 34-year-old paediatric nurse living in Dublin, was told at her 12-week scan in 2009 that a large part of her baby's skull and brain were missing and that it would not survive. "I said [to the consultant] 'What do we do now?' And he said you either continue with the pregnancy and the baby might die within the next 28 weeks, or else it will die during labour or else as soon as it's born.

"So I remember asking if you have any other choices and he said, 'You can choose not to continue with the pregnancy but in that case you will have to travel to the UK.' And that is when our world fell apart."

Under an amendment to the Irish constitution in 1983, even an embryo after conception is officially an Irish citizen.

Niamh Ui Bhriain, a spokeswoman for the Life Institute, one of the most militant of the anti-abortion groups, said they planned to recruit thousands of citizens to lobby Fine Gael members of parliament to stage a backbench rebellion against any government move to liberalise the abortion ban.

"The party promised it would oppose the introduction of abortion in Ireland and we will hold them to that promise. Our volunteers will be used to make phone calls, demonstrate and lobby Fine Gael TDs, whom we believe the majority of oppose abortion," Ui Bhriain said.