UK Home Secretary Theresa May set out her beliefs in the "three pillars of Conservatism" on Saturday 9 March, amid growing rumours that she intends to try to oust Prime Minister David Cameron as leader of the Conservative Party.

Speaking at an event for the ConservativeHome website, the Home Secretary said "security, freedom and opportunity" are at the root of her political vision.

She said: "To win, we must remember our attributes as a party when we're at our best and our strongest. We're at our best when we don't try to recreate the past but adapt our policies to the needs of the day - while continuing to root those policies in our values."

In a speech likely to appeal to the party's disillusioned right, she reiterated her party's commitment to repeal the Human Rights Act if it wins the 2015 election, but also signalled the possibility of Britain withdrawing from the European Convention on Human rights altogether.

"We need to stop human rights legislation interfering with our ability to fight crime and control immigration," May said. "That's why, as our last manifesto promised, the next Conservative government will scrap the Human Rights Act.

"I want to be clear that all options - including leaving the Convention altogether - should be on the table."

She also set out her views on subjects from welfare reform to financial services at the Victory 2015 conference, organised to discuss Tory strategy for the next general election, and said the Tories would claim victory by being "the party for all".

Reaction on Twitter was mixed.

Political philosopher Philip Blonde tweeted: "Theresa May's speech not 'I want to be leader' but rather 'I could be.'"

Activist Brian Cooke tweeted: "Great speech from Theresa May. I have a feeling I'm listening to the next leader of the Conservative party and maybe the second female PM."

The speech comes after a week of rumours that May is planning to challenge for the leadership of the party, in the wake of the Eastleigh by-election, in which the Conservatives slipped into third place behind Ukip.

May has made a number of recent moves observers believe are designed to woo the party's disillusioned right, and this week announced plans to compel immigrants to pay a bond to make sure they leave the country when their visa expires.

But one party right winger told the Guardian yesterday that the rumours were being circulated by chancellor George Osborne to undermine May, who is leading a group of ministers who have dubbed themselves the Ministers' Union, and oppose further spending cuts to their departments.

During Prime Minister's Questions this week, opposition leader Ed Miliband taunted the Tories over the May rumours, saying he "looked forward to facing her when they are in opposition".

Backbenchers are believed to be prepared to launch a vote of no confidence in Cameron if the Tories fare poorly in the May local elections and the chancellor's budget is badly received.

A contest will be sparked if 46 backbenchers write to the Conservatives' 1922 Committee, requesting a party leadership vote.