Michael Gove has set out a prime ministerial vision of a compassionate Conservatism that champions aspiration in a speech that will fuel speculation about his leadership ambitions.

In the sort of speech that is normally delivered by a prime minister, the education secretary said the "animating mission" of Tories in government was to ensure people from all backgrounds led fulfilled lives.

Gove, who touched on no fewer than 11 policy areas, made his remarks in the annual Keith Joseph memorial lecture organised by the Centre for Policy Studies, the Thatcherite thinktank that was the intellectual powerhouse behind her government. Joseph, Thatcher's intellectual guru, was seen as the leading contender on the right to replace Ted Heath until he warned in a notorious speech in 1974 that "our human stock is threatened" by low income young mothers.

He said the government should follow in the footsteps of Joseph, who had championed deprived people throughout his political life. He said: "Thanks to the leadership shown by David Cameron, our party has a social philosophy imbued by the spirit of Sir Keith's great work – consciously in the tradition of compassionate conservatism he incarnated.

"That is why I believe the best memorial we can erect to him is a society in which opportunity is more equal, the needs of the most vulnerable are our first priority and the greatest fulfilment any of us can have is in service to others."

Gove's decision to launch a raid on territory occupied by other members of the cabinet will raise eyebrows among Tory MPs who do not believe his protestations that he has no interest in the leadership.

The education secretary maintains that he is motivated by a simple belief that Conservative ministers, including David Cameron, appear woefully incapable of explaining how this is one of the most radical governments in a generation.

He said he was spoiling for a fight with the left and defended his education shakeup, Andrew Lansley's health service reforms and the way Iain Duncan Smith is changing the welfare system.

He said: "In office Iain's work has been transformative. The welfare system has been reformed – not to save money but to save lives. Instead of incentives for idleness and a culture of dependency, there are powerful incentives to work, to provide for others, to achieve fulfilment."

But Gove also made clear he was happy to to battle with the right as he defended the planning reforms of Nick Boles which are being fought by the Daily Telegraph among others. Gove, a close friend and ally of Boles, said that anyone who believes in aspiration must believe in increasing the housing stock to help bring down house prices.

• This article was amended on 17 May 2013 to change the start of the second paragraph from "In a speech…" to "In the sort of speech…".