Charities and an MP are campaigning for tougher restrictions on sex offenders, saying the system is not preventing the grooming and exploitation of children.
The "Childhood Lost" campaign says police also need powers to restrict suspects who have not been convicted.
Nicola Blackwood MP is tabling an amendment to a bill to create Child Sexual Abuse Prevention Orders, similar to anti-social behaviour orders.
The Home Office said that it would consider the campaign's proposals.
The UK has a range of powers designed to control sex offenders, including a general requirement that they inform the authorities of their whereabouts.
The main restrictive power, the Sexual Offences Prevention Order (Sopo), can curtail a convicted offender's movements, such as by banning them from parks or from near schools.
But critics say it is hard to impose conditions if they are not immediately sought during sentencing, and impossible for the police to seek to restrict the behaviour of a suspect who hasn't been convicted.
Police forces rarely seek Foreign Travel Orders against offenders who go overseas to abuse children because the courts can only ban travel in limited circumstances.
Ms Blackwood said that the proposed Child Sexual Abuse Prevention Order, to be introduced as an amendment to the Antisocial Behaviour Bill, could simplify the current system and allow police to pursue grooming gangs more vigorously.
The Oxford West and Abingdon MP said she was backing the campaign in the wake of the shocking scale of grooming in her own constituency, exposed in a major trial earlier this year.
The men at the heart of that sex grooming ring - and others like it in other cities - spent weeks and months grooming vulnerable girls before trafficking them into a life of prostitution.
Ms Blackwood said: "As an Oxford MP, I have seen for myself the appalling devastation caused by child sexual exploitation. Victims were not only targeted by abusers but also failed by those supposed to protect them. That must end now.
"The current prevention orders do not give police the tools they need to prevent child sexual abuse. The law is still failing victims."
Under the campaign's proposals, police chiefs could seek an order using hearsay evidence and other intelligence about a suspected offender, even if the apparent victim is too afraid to co-operate.
The court could then ban a suspect from any activity linked to abuse - such as having children in their cars, or entering areas where they are known to target them. Individuals would face up to five years in jail if they break the order.
A Home Office spokesman said: "Whilst we have some of the toughest powers in the world to deal with sex offenders, we keep them under constant review and will consider proposals like this.
"We are already looking to improve the use and effectiveness of Foreign Travel Orders and other measures to put further protections in place."
The coalition of charities behind Childhood Lost also wants each area to have a dedicated child sexual exploitation centre to identify and protect victims. It also wants ministers to have the power to publish internal local council reports into serious failures by social services.