The Police, Crime, Sentencing and Courts Bill is a near 300-page piece of proposed legislation covering the government’s flagship crime and justice plans.
Among the bill’s many measures are plans to introduce tougher sentences for the worst crimes, while also stopping the automatic early release from prison of serious and violent sexual offenders.
Critics fear it could be used to curtail the rights of people to protest, while ministers say the "tough" legislation will help keep people safe and contains vital reforms.
Sky News takes a look at what is in the legislation and why some are calling for it to be amended in the wake of Ms Everard’s killing.
What are the key measures?
• The maximum sentence for assaulting an emergency worker will be doubled to two years, while a Police Covenant will be enshrined in law to protect serving and retired officers and their families.
• Whole Life Orders for the premeditated murder of a child, which will also allow judges to give the maximum sentence to 18 to 20-year-olds in exceptional cases, such as for acts of terrorism leading to mass loss of life.
• The ability to stop the automatic early release of offenders who pose a danger to the public and scrapping the automatic release halfway through a sentence of serious and violent sexual offenders.
• Life sentences for killer drivers
• Widening position of trust laws to make it illegal for sports coaches and religious leaders to engage in sexual activity with 16 and 17-year-olds in their care.
• Increasing the maximum penalty for criminal damage to a memorial, from three months to 10 years.
• Reversing bail reforms which have seen suspects accused of serious and violent crimes being released without restrictions and instead imposing conditions if they could pose a risk to victims, witnesses or the public.
• Police could be allowed to obtain search warrants to help find human remains where a prosecution is not possible, such as where a suspect has died, is unfit to plead or has already been convicted in absence of a body.
Why is there renewed scrutiny of the bill?
It will significantly beef up police powers to crack down on protests.
One of the provisions of the legislation is giving police forces more powers to tackle "non-violent" protests which are significantly disruptive to the public or on access to parliament.
An offence of "intentionally or recklessly causing public nuisance" is included in the bill.
Someone commits this offence if they cause "serious harm to the public", which can include "serious annoyance, serious inconvenience or serious loss of amenity". If convicted, individuals could be hit with a fine or face a prison sentence.
Officers could also be given more powers to impose conditions on static protests, such as time and noise limits, as well as extending those rules to one-person demonstrations.
Officers could also be given more powers for tackling unauthorised encampments which interfere with the ability to use the land.
Stop and search powers could also be expanded, if plans for serious violence reduction orders get the go ahead.
This would mean it would be easier for police to carry out checks on individuals who have been convicted of carrying a knife before.
How close is the bill to becoming law?
On 16 March, MPs voted 359 to 263 – a majority of 96 – at the second reading of the Police, Crime, Sentencing and Courts Bill.
It means the legislation moved on to the next stage in the parliamentary process and is a step closer to becoming law.
MPs will continue to consider the legislation in the coming weeks, before it passes to the House of Lords.
What are critics saying?
Labour voted against the legislation at its second reading.
Although they support several measures in the bill, Labour argue it will impose disproportionate controls on free expression and the right to protest.
The party’s shadow justice secretary, David Lammy, said the suspected murder of Ms Everard had "instigated a national demand for action to tackle violence against women" and so it was "no time to be rushing through poorly thought-out measures to impose disproportionate controls on free expression".
He said the legislation was a "mess" which could lead to tougher penalties for damaging a statue than attacking a woman.
Labour leader Sir Keir Starmer said: "It says lots of things about statues and almost nothing about protecting women and girls, and particularly dealing with violence against women and girls.
"This is a crime, police, sentencing and court bill, it should be the vehicle for addressing it. And there is nothing meaningful in it."
Sir Keir added there was a "gaping hole" in the legislation and said it "doesn’t address the fact that sentencing for rape and stalking is too low".
The party wants the government to drop the bill and work on a cross-party basis to tackle violence against women.
Some backbench Conservative MPs have also voiced their unease with the provisions in the bill.
Former prime minister Theresa May said she feared the "potential unintended consequences of some of measures in the bill, which have been drawn quite widely".
Sir Graham Brady, chairman of the 1922 Committee of backbench Tories, urged Home Secretary Priti Patel to "make sure that the legislation that we’re about to pass protects that right of peaceful protest and only stops serious disruption".
What has been the government’s response?
Prime Minister Boris Johnson has said the bill includes new measures to toughen sentences for rapists, to stop the early release of serious sexual and violent offenders, and to toughen the law on domestic violence.
After a meeting of the Criminal Justice Taskforce, the government said that plain clothes police officers could patrol bars and nightclubs around the country as part of plans to protect women from "predatory" offenders.
Doubling the funding provided to the Safer Streets fund to £45m is part of a move to take "immediate steps to provide further reassurance" for women and girls in the wake of the killing of Ms Everard.
Mr Johnson said the "horrific case" had "unleashed a wave of feeling about women not feeling safe at night".
"We must do everything we can to ensure our streets are safe, and we are bringing in landmark legislation to toughen sentences and put more police on the streets," the PM said.
Amanda Milling, co-chairwoman of the Conservative Party, said Labour’s move to oppose the crime bill was "shocking", accusing the opposition of "trying to block tough new laws to keep people safe, including many vital measures to protect women from violent criminals".
"By voting against this bill, Labour are voting against tougher sentences for child murderers and sex offenders, killer drivers and measures that protect the vulnerable," she said.
"This Conservative government is working to keep people safe by reforming our justice system to keep our communities safe so that everyone can live their lives free from the fear of crime."