David Cameron is to seek to reassure restive Tory activists by promising to foster "aspiration" and give school sport a £150 million cash boost.

The Prime Minister is addressing the party's spring forum after a turbulent fortnight following the disastrous Eastleigh by-election. He has suffered a damaging bout of leadership speculation and pressure to move the party to the right after being beaten into third place there by Ukip.

The speech comes just days before a Budget which is seen by MPs and many party members - along with May's local elections - as a key test of his leadership. Mr Cameron will tell activists his approach chimes with the Tory values of highly-popular figures such as Margaret Thatcher and Winston Churchill as he attempts to steady the ship.

"The global race is not just about GDP," he will say. "It's about saying to the mum who's worried about her children's future, we are building a country where there is a future, so your kids won't have to get on a plane to get on in life, they can make it right here in Britain. It's what this party's always been about - aspiration."

In a swipe at Labour opposition to tough benefit cuts being rolled out as part of the deficit reduction, he will paint them as "patronising people, patting them on the head and putting a benefit cheque in their hands". Instead the Government was "giving people the tools to succeed."

Mr Cameron - who has come under fire from backbenchers over his "posh, male and white" inner circle - will acknowledge the "leg-ups" he enjoyed in life. "I know the leg-ups I got in life. A loving family, wonderful parents, a great school and university. We want people to climb up through their own efforts, yes, but in order to climb up they need the ladder to be there in the first place, the family that nurtures them, the school that inspires them, the opportunities there for them.

"Great Conservatives down the generations have put those ladders in place. When Churchill invented the labour exchanges that helped people into work. When Macmillan built new homes. When Thatcher fired up enterprise so people could start their own businesses. That's what we're doing in the Conservative Party right now."

Home Secretary Theresa May - who last week fuelled leadership ambition speculation with a speech which ranged far beyond her policy brief - is also addressing the forum. She is reported to have been the target of Education Secretary Michael Gove's private warning to Tory Cabinet ministers earlier this week not to undermine David Cameron's position as PM. But her speech is expected to be restricted to home affairs issues.

London Mayor Boris Johnson had earlier told Conservative Cabinet ministers accused of positioning themselves for the post-Cameron leadership to "put a sock in it and back the Prime Minister".

Mr Cameron will come under renewed pressure to abandon moves to legalise same-sex marriage - which opponents warn is leading activists to abandon the party in droves and is losing it large numbers of votes. Several backbenchers spoke out on Saturday in support of the "Conservative Grassroots" group set up to campaign on the issue and for "core Conservatives values" in the wake of a major Commons rebuke to the premier on gay marriage.