More than 150 organisations have warned ministers that a new law handing police tougher powers to crack down on protesters would be “an attack on some of the most fundamental rights of citizens” as Labour vowed to oppose it and officers’ handling of a vigil for Sarah Everard continued to draw criticism. The groups, including human rights charities, unions and faith communities, said on Sunday the wide-ranging legislation would have a hugely detrimental effect on civil liberties, and called for the government to “fundamentally rethink its approach”. In a letter to the home secretary, Priti Patel, and the justice secretary, Robert Buckland, seen by the Guardian, they claim the 307-page police, crime and sentencing bill – being debated on Monday and Tuesday before a vote – is being rushed through parliament before people have “been able to fully understand its profound implications”. Some of the new police powers are draconian, they said, cautioning that the new law would also increase penalties for those breaching police conditions on protests and the ease with which they can be found to have done so. They said it raised “profound concern and alarm” and would also threaten access to the countryside and criminalise Gypsy and Traveller communities, adding that the legislation is being “driven through at a time and in a way where those who will be subject to its provisions are least able to respond”. Signatories to the letter include Liberty, Big Brother Watch, Unite, the End Violence Against Women Coalition, Unlock Democracy, Cafod and Extinction Rebellion local groups. The letter comes after the Labour leader, Sir Keir Starmer, made a significant intervention on Sunday, telling his MPs to vote against the bill. Sources said it was a switch in tactics from the previous plan to abstain. He said the bill contained “next to nothing” on countering violence against women and girls, after complaints that police at a vigil for Everard in south London on Saturday were too heavy-handed. Starmer lamented that the legislation said “lots of stuff on statues” – new offences are being created for those who destroy or damage a memorial – and called it a missed opportunity for the government. The Conservatives hit back, with the party’s co-chair Amanda Milling claiming that voting against the bill would block “tough new laws to keep people safe, including many vital measures to protect women from violent criminals” and “tougher sentences for child murderers and sex offenders”. In a sign of growing anger, Jess Phillips called Milling’s response a “disgusting and untrue statement”. “The Conservative government’s bill does absolutely nothing currently to increase sentences for rapists, stalkers, or those who batter, control and abuse women,” the shadow domestic violence minister said. “It does nothing about street harassment and assaults. The bill is full of divisive nonsense like locking up those who damage statues for longer than those who attack women.” Some Tory MPs have serious reservations about the bill, which they plan to raise in the debate this week, the Guardian understands – but there is unlikely to be a substantial enough rebellion to bring a defeat for the government. One Tory backbencher said the legislation was necessary as it had been drawn up in response to protests by Extinction Rebellion and covered many areas, from child sexual abuse offences to ensuring that vehicles could enter and leave the parliamentary estate. The part of the bill that has caused opponents most concern will give the home secretary powers to create laws to define “serious disruption” to communities and organisations, which police can then rely on to impose conditions on protests. The Home Office said it was needed to counter “highly disruptive tactics used by some protesters” that “cause a disproportionate impact on the surrounding communities” and said Extinction Rebellion’s “April uprising” cost the Metropolitan police more than £16m. It denied that freedom of expression would be undermined by the bill, saying: “The majority of protests in the England and Wales are lawful and will be unaffected by these changes. These measures will balance the rights of protesters with the rights of others to go about their business unhindered. They will achieve this by enabling the police to better manage highly disruptive protests.” Labour MP and former solicitor general Harriet Harman is meanwhile trying to amend the bill to outlaw kerbcrawling and stop women’s previous sexual history being used in evidence in court. She urged the government, after it reopened its consultation into countering violence against women and girls, to create a “bespoke” bill, saying: “We will achieve much greater progress if we work by consensus.”