Demonstrators took to the streets of central London for a third straight night following widespread criticism of the Metropolitan Police’s handling of the vigil for Sarah Everard at Clapham Common on Saturday.
Activists chanted “kill the bill” as some carried banners, including one which said “the right to protest is a human right” outside Scotland Yard.
It came as the Police, Crime, Sentencing and Courts Bill passed its second reading in the Commons by 359 votes to 263. It will now undergo further scrutiny at a later stage.
The Foreign Secretary said that while new measures are being introduced, it was appalling that women still suffered fear, intimidation and threats.
Speaking on Sky News Mr Raab said: “I think it is appalling that women still suffer the fear, the intimidation, the threats – and I say that as a son, a husband and a brother of a sister.
“And that’s why we are increasing the number of police by 20,000, we’ve heard new measures to make the streets safer with CCTV and lighting overnight, we’ve got two bits of legislation going through the House of Commons to increase the sentencing.
“I was a justice minister twice – I’ve been looking at those issues, I worked on the regional increase in stalking sentences. But clearly we’ve got to do more.”
Four people were arrested and two received fixed penalty notices over Monday’s protests, but a Met spokesman said he was not aware of any issues on Tuesday.
As part of efforts to overhaul the justice system, the Government has proposed a raft of changes in the Bill.
These include plans to give police in England and Wales more powers to impose conditions on non-violent protests judged to be too noisy and thereby causing “intimidation or harassment” or “serious unease, alarm or distress” to the public.
Time and noise limits could be imposed as a result of the measures in the Bill and those convicted could face a fine or jail.
As the bill was debated Labour MP Clive Efford (Eltham) claimed in the Commons: “We’re witnessing a Tory-led coup without guns.”
Labour former justice minister Maria Eagle added: “This populist Government has swiftly developed a penchant for authoritarianism.”
Shadow justice secretary David Lammy said: “The truth … is (the Government) is introducing these measures because it dislikes Black Lives Matter, because it hates Extinction Rebellion, because both tell too many hard truths.”
For the Government, Justice Secretary Robert Buckland accused Labour of putting “party interests before the national interest” by attempting to block the Bill.
Additional reporting by PA