Scottish Conservative leader Ruth Davidson has called for greater help for homebuyers and more free nursery places for two-year-olds in a keynote speech designed to broaden the appeal of her party beyond "people who have made it".

She told supporters in Glasgow that the Bank of England should indemnify high street lenders, allowing a return to 95% mortgages and letting buyers get on the housing ladder without the high deposits required since the 2008 financial crash.

She also backed calls to extend free nursery places to two-year-olds, starting with those from the most deprived backgrounds, and develop vocational teaching in schools for 14 and 15-year-olds.

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The moves, she said, were part of her party's guiding principle to give everyone "a fair crack of the whip" in life and reward hard work, aspiration and responsibility.

Ms Davidson – who earns £57,500 as an MSP – revealed she was still saving for a deposit on a home. She added: "It is wrong that mortgages are no longer available to people who can afford to make the monthly repayments but who suddenly –as a knock-on effect of irresponsible bank lending in the past – are required to have at least a 20% or 30% deposit instead of a 5% deposit."

Ms Davidson said later she had raised the issue with the Prime Minister and Treasury officials and hoped to see the measure included in Chancellor George Osborne's Budget next month.

On the issue of childcare, she said: "If Scotland's working families are to get a fair crack of the whip then we must redouble our efforts to increase the availability and reduce the costs of childcare." She called for a commitment to extend free nursery places to all two-year-olds – a move that would cost £130 million per year – starting with the 40% most disadvantaged.

Ms Davidson also used her speech to reiterate the Scottish Conservatives' desire to use Holyrood's new tax powers, coming into force from 2016, to cut the basic rate of income tax by 1p.

The measure, which she claimed would boost the economy, would cut Scottish Government revenue by £500m.

Speaking after her address at Glasgow's Mitchell Library, she said a range of services and benefits would be cut to meet the shortfall. Cash for councils was likely to be cut and free eye tests axed under future Conservative plans, she warned.

Free university tuition and free prescriptions were also likely to be dropped in the party's 2016 Holyrood manifesto, though the money saved would be ring- fenced for higher education and the health service respectively.

The plans emerged in the first of three speeches explaining the Tories' direction under Ms Davidson, who became leader 15 months ago.

In a highly personal passage, she described how she worked in an amusement arcade in Kirkcaldy as a teenager and, as a young journalist, begged high street stores for a job after being made redundant from a radio station in Perth.

She said she did not recognise the caricature of the Scottish Conservative party as representing only those who had "made it" but admitted: "It is one reason why many Scots, while sharing the same values as us, continue to vote for other parties."