Britain's largest abortion provider has warned it is facing "a new era" in terms of the actions anti-abortion protesters are prepared to take, after it called police to one of its London clinics where women were being filmed arriving and leaving.

Activists are holding prayer vigils outside the branch of the British Pregnancy Advisory Service (BPAS) on a daily basis as part of the 40 Days for Life campaign, which is affiliated to a US anti-abortion network and whose activities have been endorsed by the more established Society for the Protection of Unborn Children.

The campaign – which has said in the past that it uses cameras to protect its members from attack – attempted to distance itself from the incident involving police on Monday, saying the cameraman was not associated with it and meant no harm.

It comes after a West Midlands man pleaded guilty on Saturday to hacking into the BPAS website. The organisation now says it will seek a meeting with the Department of Health to raise concerns about the current climate of anti-abortion activism.

A BPAS spokesperson said recent political initiatives by some MPs had contributed to the changing climate. "The language that has been used by MPs very definitely has consequences in terms of what protesters are now saying to women outside of our clinics," she said.

"A culture seems to be being fostered where protesters (when they are not filming) think it is entirely acceptable to harangue women outside centres and tell them if they go inside they will be lied to. There is certainly evidence of women being really quite distressed and feeling intimidated on what can already often be quite a difficult day for them."

She said BPAS was reluctant to embrace US pro-choice actions such as having volunteers escort women past protests, but the presence of anti-abortion activists outside the BPAS clinic in Bedford Square on one recent day had been such that members of the public had intervened to escort women inside.

On Tuesday, a solitary participant in the 40 Days for Life campaign was reciting the rosary across the road from the clinic. On the ground beside him was a large banner that read: "Praying for an end to abortion and offering help," as well as a box containing a number of small plastic foetuses. At other times, the campaign's own "counsellors" approach women on the street.

The man, who did not want to give his name, said he and others were there to pray for a change of heart on the part of women coming to the clinic.

"I've been here since the morning. I keep my distance and hand out some of our leaflets and magazine. There was a lady here this morning and she said that she was going to keep her baby after all and that made what we are doing over 40 days entirely worthwhile," he said.

The campaign used Twitter to announce this week that it had achieved its first "turnaround" outside the clinic, claiming that a woman named Melanie had decided not to go ahead with her visit. Other turnarounds were said to have taken place in Brighton.

The organisation has called for a big turnout on 30 March when, it said, a vigil would be led by the Catholic bishop of Westminster, Alan Hopes.

Other anti-abortion organisations have held gatherings outside abortion clinics in recent days. Activists said more than 170 people took part in a vigil outside a BPAS clinic in east London on Saturday organised by Helpers of God's Precious Infants UK, a Catholic group, with the support of local churches in the area.

The official representative of the local Catholic bishop, Thomas McMahon, read out a letter of support during an opening mass. In Brighton, Abort 67 held a protest outside a clinic on Tuesday.

At the weekend, James Jeffery, who used the handle "Pablo Escobar", pleaded guilty to two offences under the Computer Misuse Act after hacking into the BPAS site on Thursday. He defaced the front page with an anti-abortion message and the Anonymous logo, and took details of people who had visited the site looking for advice.

Robert Colquhoun, a spokesman for 40 Days for Life, said: "40 Days for Life conducts a peaceful, prayerful and legal vigil in London. The central point of our vigil is to pray for an end to abortion and show that that is a love in community that can help a woman to choose life for her unborn child.

"Since our campaign started in September 2010, we estimate that more than 30 women have chosen life for their unborn children as a result of our campaign through prayer and also through an offer of love, help and support during a difficult time.

"We have a statement of peace that sets the tone and ethos of our prayer vigil as a peaceful and prayerful event. Since our campaign started, we have received a very large number of insults and threats. At times, members of the vigil have filmed themselves in order to protect themselves from these threats. We do not encourage anybody to film members of the public during our campaign."