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Women's groups are threatening to take the home secretary to court if she does not take "immediate steps" to tackle "police-perpetrated abuse of women".
They are threatening to launch a judicial review and want an independent inquiry, set up by Ms Patel, to be given statutory powers.
At present it is non-statutory, meaning it cannot compel witnesses to attend.
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It will be "denied powers to compel the production of evidence from the police, and to protect vulnerable witnesses and whistleblowers", the CWJ said.
Couzens, a serving Metropolitan Police officer at the time, used his warrant card and handcuffs to snatch Ms Everard in Clapham, south London, in March.
He was sentenced to a whole-life tariff, which he is appealing.
The CWJ said it raised "serious concerns" in a letter to Ms Patel last month, but had not received a response.
"In light of the secretary of state's failure to respond to CWJ's letter or to take steps addressing the concerns raised, we have now taken formal steps to commence the process of taking the home secretary to court," it said.
The CWJ's solicitor, Debaleena Dasgupta, said: "We wrote to the home secretary less formally over three weeks ago requesting urgent action. We are disappointed that not only has she failed to take any action, but she has failed to even respond.
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"These are not the actions of a home secretary committed to speedily tackling police-perpetrated abuse of women."
CWJ director Harriet Wistrich said "police-perpetrated abuse of women" had become a "national scandal that demands an urgent and appropriate response".
A Home Office spokesman said the inquiry could be "converted to a statutory inquiry if required" and that "further detail will be set out in due course".
They added: "The public have a right to know how this happened, which is why the inquiry will establish this first, before looking across policing more broadly to ensure something like this can never happen again."
Last week, two Metropolitan Police officers pleaded guilty to sharing photos of the bodies of two murdered sisters on WhatsApp.
Met Police Commissioner Dame Cressida Dick has admitted there is "unwitting sexism" within the force.
She also ruled out resigning following Couzens' conviction.