Ealing Council was the first in the country to create a 100-metre protest-free "buffer zone" outside a Marie Stopes clinic in the west London borough after pro-life activists were accused of intimidating the clinic's patients.
The vigil members deny the claims and say they simply pray and offer patients counselling and other options besides abortion.
Mr Justice Turner decided to allow the ban on 2nd July after Christian mother Alina Dulgheriu challenged it.
He said the council was "entitled" to conclude it was a "necessary step in a democratic society".
Dulgheriu has started an online fundraiser to pay for legal costs to appeal the ruling. It has received more than £14,000 in six days.
"I do not have the financial resources to challenge the PSPO in the Court of Appeal, and without your support, I can't bring an appeal," Dulgheriu said.
She added she was offered help and support when entering an abortion centre by a pro-life vigil in 2011.
"I was given another choice which meant that I could have my beautiful daughter," she said.
"Since then I have regularly attended vigils in London to offer the same help and support to other women in need, as many women who go to an abortion centre do not want an abortion."
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