Any act which shows disapproval of the termination of babies is prohibited outside the area around the Marie Stopes centre.
This includes vocalised prayer.
Alina Dulgheriu, a mother who was supported by a pro-life vigil outside a London abortion clinic, took action against Ealing Council last year but the Public Spaces Protection Order (PSPO) was upheld.
She has since launched a crowdfunding campaign to fund the ongoing appeal, which successfully raised over £50,000 in under three months.
Responding to the verdict, Alina said: "I am delighted that Court of Appeal will be reconsidering the very disappointing decision of the High Court.
"My little girl is here today because of the real practical and emotional support that I was given by a group outside a Marie Stopes centre, and I am continuing with this appeal to ensure that women in Ealing and all across the country do not have this vital support option removed."
Elizabeth Howard from the pro-life group Be Hear for Me, which is supporting Alina, told Premier: "The PSPO, as it currently stands, is utterly draconian.
"It's truly shocking that, in the 21st century, prayer has been banned in a public and that just simply saying to someone 'can I help you' is banned in a public place."
Click here to listen to Premier's Alex Williams speaking with Elizabeth Howard:
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