The Conservative party in the UK is prepared to withdraw from the European convention on human rights (ECHR) after the next election, the home secretary Theresa May has said, as she detailed a fresh drive to curb the appeal rights of 70,000 people who face deportation every year.

"The next Conservative manifesto will promise to scrap the Human Rights Act. It`s why Chris Grayling is leading a review of our relationship with the European court [of human rights]," she told the party`s conference. "And it`s why the Conservative position is clear – if leaving the European convention is what it takes to fix our human rights laws, that is what we should do," she said to applause.

May was followed by the justice secretary, Chris Grayling, who set out a timetable for the development of their policy for a radical reform of human rights law. He said the Conservatives would publish a document in 2014 "setting out what we will do, when we will do it, and how we will do it", followed by a draft bill setting out the legal detail later in the year.

May`s explicit statement followed David Cameron`s hint on Sunday that the Tories were openly considering the "nuclear option" of withdrawing from the ECHR, despite warnings from the attorney general, Dominic Grieve, and others, of the damage to Britain`s international standing.

May also used her conference speech to confirm that illegal migrants, criminal foreign nationals and others facing deportation will have their rights to appeal severely restricted. The number of grounds on which they could appeal will be reduced from 17 to four, and the extent to which a fresh appeal could halt a deportation is to be limited.

She said unless there was a "risk of severe and irreversible harm" foreign criminals should be deported first and their appeals heard later. The moves are to be included in the new immigration bill, which will be published next month, and are intended to cut the 70,000 annual appeals by more than half.

The home secretary said the immigration bill would also put into primary legislation guidance that had already gone to judges to ensure that illegal migrants and others cannot abuse article 8 – "the right to a family life" – to prevent their deportation from Britain.

"Some judges chose to ignore parliament so I am sending a very clear message to those judges," said May. "Parliament wants the law on people`s side, the public wants the law on the people`s side and the Conservatives in government will put the law on the people`s side once and for all."

The home secretary, speaking in a hall with posters boasting that the Conservatives had cut immigration, claimed only her party could be trusted on immigration. She said the annual number of overseas student visas issued had been cut by more than 115,000.

But May admitted frustration with her Liberal Democrat coalition partners over her proposal to introduce a £3,000 visa bond that visitors would forfeit if they failed to leave the country in time. She said that despite being a Conservative manifesto commitment, the Lib Dems had first claimed it as their idea, then backed it, then blocked it. She confirmed that the proposal remained deadlocked in coalition talks.

May said the government would push through a fresh drive against human trafficking with the publication soon of a "modern slavery bill". She said the legislation would bring together a confusing array of human trafficking offences into a single act, giving police and prosecutors the power to investigate, prosecute and punish "modern-day slavedrivers". The legislation is expected to introduce a lifetime ban on those convicted of human trafficking offences from working as "gangmasters" employing migrant labour.

Grayling also hinted at frustration with coalition politics as he confirmed his weekend announcement to end the use of cautions for serious violent and sexual offences. However, he could only say that his aim of ending automatic release for prisoners serving determinate sentences of four years or less was next on his "task list" – presumably subject to negotiation with the Lib Dems.