Volunteers from Abort67 have been gathering outside various clinics in recent months holding placards with images of unborn foetuses.
The British Pregnancy Advisory Service (BPAS) said "an abortion clinic is to close as a direct result of protest activity" but denied the clinic was one of its own.
Abort67 has described the development as a "result" for its campaign but denied it was intimidating women who attend the clinics.
"All that's happening, if it's one of the clinics that we're standing outside of, is we're holding up pictures of what abortion would do to the unborn child," said Abort67 spokesman Andy Stephenson to Premier.
"It's absolutely untrue that we're filming women going into abortion clinics but it certainly creates a better supporting story to create the idea that we're filming women, which I think is rather cruel."
Abigail Fitzgibbon, head of advocacy and campaigns at BPAS, said: "It is absolutely despicable that any group should resort to the harassment of individuals in order to close down an NHS service they personally disagree with.
"Whatever our beliefs about abortion we should all agree that women do not deserve such treatment at such a difficult time in their lives. If clinics close and women cannot access legal abortion women will look to illegal and potentially unsafe means to end their pregnancies."
Andy Stephenson, Abort67 speaking to Premier Des Busteed:
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