The Marie Stopes abortion clinic in Ealing was the first in the country to introduce a Public Spaces Protection Order (PSPO) of 100 metres around it, supported by their local MP Rupa Huq.
Those standing outside abortion clinics were mostly from pro-life group the Good Counsel Network, who tried to help women change their minds and offer practical support when financial or domestic pressures were leading women towards termination.
Pro-choice groups began turning up in 2005, protesting against the pro-life group's presence, the judge described the combination of the two groups by saying it 'generated an atmosphere of tension outside the Centre'.
The buffer zone was challenged last year at the High Court, with the judge concluding that it was a "necessary step in a democratic society".
Alina Dulgheriu and Andrea Orthova from the Good Counsel Network are now challenging that decision in the Court of Appeal infront of three senior judges.
A group of mothers who say they were helped by vigil members outside abortion clinics rallied outside the Royal Courts of Justice while the hearing was taking place.
The public spaces protection order (PSPO) came into force in April after reports of "intimidation, harassment and distress" for women using the facility in Mattock Lane.
Clinical operations manager John Hansen-Brevetti said women had been told the ghost of their foetus would haunt them, had been told "mummy, mummy, don't kill me", had holy water thrown on them and rosary beads thrust at them.
Ruling on the case in July last year, Mr Justice Turner said: "There was substantial evidence that a very considerable number of users of the clinic reasonably felt that their privacy was being very seriously invaded at a time and place when they were most vulnerable and sensitive to uninvited attention.
"It also follows that, in this regard, I am also satisfied that the defendant (council) was entitled to conclude that the effect of the activities of the protesters was likely to make such activities unreasonable and justified the restrictions imposed."
The judge said his ruling did not give the "green light" to local authorities to impose PSPOs around all abortion clinics and each case must be decided on its own facts.
Ms Dulgheriu says she was offered financial, practical and moral help, as well as accommodation, and now has a "beautiful" daughter.
In a statement following the ruling, she said: "I am saddened and shocked that the court has upheld a PSPO that prevents good people giving help to mothers who desperately want it.
"I am devastated for those women that, since the introduction of the Ealing PSPO, have not been able to access the loving help that I did.
"I feel desperately sorry for the vigil members who since the move to create this PSPO have been consistently subject to abuse on the street and slander online."
Ealing Council leader Julian Bell said at the time of the ruling: "This sends a clear message to those that have denied that there is evidence of unacceptable behaviour having a detrimental impact on people in this area, that there was a problem and action needed to be taken.
"The harassment and intimidation of local residents and those accessing legally available medical services was totally unacceptable and 'the feelings of intrusion' was clearly having a negative impact.
"Since the safe zone was implemented in April, we have seen a dramatic reduction in anti-social behaviour, confirming to us that we were right to take this action in the interest of those people living in the locality of Mattock Lane, and for those who visit the area."
Additional reporting by Press Association.
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