Marie Stopes International has said it will temporarily stop providing a number of services after the Care Quality Commission raised concerns about patient safety.
Around 250 women requesting abortions a week will be affected, NHS England said. Those affected will be sent to different services.
Right To Life, a charity campaigning against abortion, said the move was "gladdening to say the least".
Executive Officer and Christian Peter D. Williams said: "We have long heard from anecdote that the manner in which Marie Stopes has provided its 'services' has been at times abusive and left women aggrieved at what is already a very difficult time.
"It is gladdening to say the least to see that the CQC has stopped Marie Stopes abortion provision.
"Abortion is always destructive of the lives of unborn children, but when prosecuted as it has been by some abortionists, it can leave women scarred as well.
"I hope this opens a real debate about the under-regulation of abortion in the UK; one that leads to a proper respect and application of the original intention of Parliament in 1967 and the welfare of women - and increasingly their unborn children - to be made paramount".
After the inspection of Marie Stopes' services the Care Quality Commission said it had "specific immediate concerns" around consent and safeguarding.
Training and competence for terminations were not satisfactory, it said.
Prof Sir Bruce Keogh, national medical director at NHS England, said: "This will be an anxious time for those women affected and we are taking immediate action to ensure everybody involved has access to the appropriate confidential advice and services."
Simon Cooke, Chief Executive, Marie Stopes International, said: "As of Friday 19th August, Marie Stopes UK has agreed with the Care Quality Commission (CQC) to voluntarily suspend some of its termination of pregnancy services. This is to allow Marie Stopes UK to resolve areas of concern in its training and governance procedures. We are working urgently with the CQC on these areas and intend to regain full assurance within a few days.
"Alongside this, our immediate priority is to make sure that women booked into one of our affected services are rebooked swiftly into alternative local services and we are working closely with NHS England to ensure that this happens.
"We'd like to reassure people that our other services remain unaffected. Each year 70,000 women are treated within our centres, and our clinical outcomes continue to outperform the national average."
