Two Catholic midwives who contested their duty to be involved in abortion procedures are today having their case reviewed by the Supreme Court in London.

Five justices will decide whether Mary Doogan and Connie Wood, both of Scotland, are able to withdraw from any involvement in a practice which they believe would "'violate their conscience".

The court appearance today follows their landmark victory last year, in which a court of appeal in Edinburgh ruled that the women had a right to refuse to delegate, supervise or support staff involved in terminations.

They had previously been denied this right, when a judge in 2012 ruled that their human rights had not been violated because they were not directly involved in the procedure.

At the time, judge Lady Smith said: "Nothing they have to do as part of their duties terminates a woman's pregnancy. They are sufficiently removed from direct involvement as, it seems to me, to afford appropriate respect for and accommodation of their beliefs."

However, the overturning of this ruling was last year supported by the Roman Catholic Church in Scotland. Archbishop Philip Tartaglia of Glasgow said it was a "victory for freedom of conscience and for common sense".

"The midwives are to be commended for their courage and determination in standing up to an unjust requirement of the employer that they be involved in abortion procedures. As the judges state, the right of conscientious objection extends not only to the actual medical or surgical termination but to the whole abortion process," he said.

"I hope that many pro-life health professionals will take heart from this judgement and have the courage to express their own objections if and when they are asked to carry out tasks which are morally wrong and violate their conscience.

He added: "Respect for workers' freedom of conscience is a hallmark of a civilised society."

The right to conscientious objection is protected by the 1967 Abortion Act. However, some health professionals are concerned about the wider implications of allowing midwives to abstain from all complicity.

"bpas [British Pregnancy Advisory Service] supports the right of healthcare professionals to conscientious objection, not least because women deserve better than being treated with contempt by those who think they are sinners. But ultimately a balance needs to be struck between that exercise of conscience and women's access to legal services," Ann Furedi, bpas chief executive, told Press Association.

"It would be grossly unjust if an interpretation of conscientious objection was allowed to stand which would disrupt services to the point that those committed to helping women were unable to do so."

Gillian Smith, Royal College of Midwives director for Scotland, also warned that changing the current law could "compromise" the care of women undergoing an abortion.

"We will be encouraging our members to continue to provide professional care to women who require this type of treatment," she said.

A spokesperson for the two organisations yesterday announced that both are "deeply concerned" that a favourable judgement for Doogan and Wood "extends the right of conscientious objection beyond the provisions intended by the Abortion Act".

NHS Greater Glasgow and Clyde is bringing the appeal today. A judgement is expected next year.