Ealing Council is due to discuss on Tuesday whether or not to impose a Public Spaces Protection Order (PSPO) that would move pro-life activists away from the local Marie Stopes centre.
The Good Counsel Network told Premier its members have been holding vigils outside for more than 23 years and their work is peaceful.
Clare McCullough from the Catholic group said: "We've been holding daily vigils there for the last four years. There have never been any incidents there. There have never been any arrests of charges made there against anybody."
PSPOs have previously been used to tackle begging and street drinking but this could mark the first time one has been implemented to deter a pro-life demonstration.
The upcoming debate by Ealing Council comes after more than 3,500 people signed a petition by the pro-choice group Sister Supporter, calling for action to deter groups like Good Counsel Network from operating outside abortion clinics.
Sister Supporter told the Daily Mail that patients - as well as people living and working in the area - have been subjected to "sustained intimidation" by anti-abortion campaigners.
Clare McCullough responded: "The whole reason for using this Public Spaces Protection Order, as they're trying to do in Ealing is because there is no harassment or intimidation, or they would be using the current laws to prosecute us.
The Good Council Network - which also holds similar vigils in other parts of London (pictured above) - said it would appeal against any bid to curtail their work outside the clinic, claiming they hand out inoffensive leaflets.
Clare McCullough added: "We have no intention of going away, so we'll fight as hard as possible to keep this freedom of speech possible and legal outside abortion centres, so that women have real options...[alternatives to abortion]."
Click here to hear Premier's Alex Williams speaking with Clare McCullough from the Good Counsel Network: