The average deposit for people buying a home will be £72,000 by 2020 if the Conservatives win another five years in power, the Labour Party will claim today.

Figures calculated by officials in the House of Commons Library show that the average house price in the UK would be £359,000 by 2020 – 13 times the average wage. Labour said this would lock hundreds of thousands of families and young people out of the housing market.

Emma Reynolds, the shadow Housing Minister, will say today that, on current trends, the gap between the demand for and supply of housing in England by the end of the 2015-2020 parliament would be 1.3m homes, the equivalent of three cities the size of Birmingham.

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The “gap” would be 383,475 homes in London; 214,875 in the South East; 156,300 in the East of England; 117,925 in the West Midlands; 114,375 in Yorkshire and The Humber; 102,350 in the East Midlands; 95,850 in the North West; 90,075 in the South West and 41,800 in the North East.

Video: What can be done to solve the housing crisis?

In the latest of Labour’s speeches spelling out “the choice” at next year’s general election, Ms Reynolds will contrast the “aspiration gap” under the Tories with Labour’s pledge to build at least 200,000 homes a year by 2020. Ms Reynolds will claim: “While the Tories say the housing market is back on track, the truth is they’ve presided over the lowest level of house building since the 1920s. We’re not even building half the homes we need to keep up with demand.”

Yesterday the Government unveiled a £3m fund to kickstart work on up to 85 housing sites and help tackle planning delays preventing the building of new homes. Brandon Lewis, the Housing and Planning Minister, said the new fund for councils would create jobs as well as up to 25,000 new homes.

He said: “In 2010 we inherited a housing industry in paralysis - where neighbours and developers were at loggerheads, aspiring home owners couldn't get on the property ladder and housebuilding levels were at their lowest since the 1920s.”