Builders should pay full council tax on homes not built before the original planning permission expires, the body, which represents local councils, said.
The BBC reports that 475,000 homes with planning permission were not completed in 2014-15, but councils were not to blame.
The government said building had started on more than half of these.
The LGA – which represents local authorities across England and Wales – said its research had found that a “bumper backlog” of homes to be built in England had “grown at a rapid pace over the past few years”.
In 2012-13, the total of “unimplemented planning permissions” was 381,390. But in 2013-14 it was 443,265, rising to 475,647 homes in 2014-15, it said.
Peter Box, the LGA’s housing spokesman, said the figures proved the planning system was “not a barrier” to house building. He said councils were approving almost 500,000 more houses than were being built.
“To tackle the new homes backlog and to get Britain building again, councils must have the power to invest in building new homes and to force developers to build homes more quickly,” he said.
“Skills is the greatest barrier to building, not planning.
“If we are to see the homes desperately needed across the country built, and jobs and apprenticeships created, councils must be given a leading role to tackle our growing construction skills shortage, which the industry says is one of the greatest barriers to building.”
A spokesman from the Department for Communities and Local Government said there had been “a 25% increase in the number of new homes delivered over the past year alone”, saying the government had “got Britain building again”.
“Alongside this we’re working closely with developers to ensure it [Britain] has the skills it needs – and saw 18,000 building apprenticeships started in 2014.
“We’re also directly commissioning thousands of new affordable homes and recently doubled the housing budget,” the spokesman added.
Sadiq Khan, Labour’s candidate for Mayor of London, said: “Under the Tories, the UK, and London in particular, has been falling far short of building the number of homes we need.
“We need powers to get developers building – alongside support for councils and housing associations which are building too.”
But John Stewart, from the Home Builders Federation, said “speeding up the rate at which permissions are granted” was one of the keys to “significant, sustainable” increases in house-building.
“Too many sites are stuck in the planning system, with an estimated 150,000 plots awaiting full sign-off by local authorities,” he said.
He dismissed claims that developers were guilty of “land banking” – or holding land in order for its value to increase.
