Councils have failed to spend almost £1m earmarked by the government for poor families at risk of homelessness, despite a growing housing crisis across the UK.

Figures show that nearly £1m of the £20m set aside to help families who could not afford rent or other housing costs in 2010-11 was left untouched by councils.

Six local authorities spent less than half the money they were allocated for these "discretionary housing payments" by the Department for Work and Pensions (DWP). They include Wirral council, which spent just £114,380 (47%) of the £245,200 the government had earmarked for the borough.

In total, £990,272 remained unclaimed in England, Scotland and Wales. Yet some councils made the decision to top up the money they received from the DWP from their own coffers, taking the total awarded to £21.4m.

The shadow housing minister, Jack Dromey, said it was up to the DWP to make sure the funding pot was properly allocated to needy families.

"With the combination of rising rents, squeezed incomes and cuts to local housing allowances and changes to housing benefit, more and more families are facing a real struggle to stay in their homes," Dromey said.

"The Department for Work and Pensions must do more together with all councils to ensure that the people affected seek advice and eligible tenants are encouraged to apply for the discretionary housing payment – which can be a lifeline for families seeking to meet shortfalls in rent in the short term or to help with moving costs."

Discretionary housing payments (DHPs) are available to people facing financial hardship who are already entitled to housing benefit or council tax benefit, but need further support in meeting the cost of housing. Most claims are made by tenants living in private rented accommodation.

The breakdown of spending across UK councils was revealed following a freedom of information request made by the housing benefit consultant Claire Turner, director of the Landlord Information Network, and covers the final year before local housing allowance rates were cut for new claimants.

In 2011-12 the government increased the total available for DHPs to £30m, while in 2012-13, when benefit cuts extend to existing claimants, it will rise to £60m.

Turner said benefit cuts made it more important for councils to publicise the payment and spend all the money they are allocated.

"Many landlords, particularly in the social rented sector, are not aware that this fund is available for tenants to claim, while their staff often aren't geared up to support tenants to make a DHP claim," she said.

However, Toby Lloyd, head of policy at the housing charity Shelter, said there was an "honest confusion" among councils about what the benefit covered. The DWP took most of the last financial year to rule whether the benefit could fund rent deposits, he said.

Citizens Advice said some councils were wary of the payments because they did not believe it was local government's role to "prop up" the benefits system. "We would rather there was a DHP system than there wasn't, but we would prefer that deficiencies in the mainstream housing benefit system were addressed at source," explained the social policy officer Geoff Fimister.

A spokesman for Wirral council said: "Applications are each considered entirely upon their own merits and the money is awarded responsibly rather than just splitting it between benefit recipients arbitrarily." Wirral Partnership Homes, the largest housing association in the area, said it sometimes helped tenants make claims, but not all these applications were successful.

Wirral

DWP allocation: £245,200

Awards made: 513

Underspend: £130, 820 (53%)

Wiltshire

DWP allocation: £139,646

Awards made: 271

Underspend: £47,086 (34%)

Cardiff

DWP allocation: £243,193

Awards made: 357

Underspend: £42,330 (17%)

Barnet

DWP allocation: £212,485

Awards made: 290

Underspend: £41,108 (19%)

Lincoln

DWP allocation: £68,851

Awards made: 195

Underspend: £33,743 (49%)

Liverpool

DWP allocation: £208,391

Awards made: 485

Underspend: £29,268 (14%)

Wolverhampton

DWP allocation: £66,365

Awards made: 112

Underspend: £27,508 (41%)

Derby

DWP allocation: £113,921

Awards made: 354

Underspend: £24,241 (21%)

Edinburgh

DWP allocation: £299,871

Awards made: 846

Underspend: £18,889 (6%)

Rother

DWP allocation: £55,521

Awards made: 153

Underspend: £17,654 (32%)

• For more on this story visit the Guardian Housing Network