Councils failed to spend more than £7m of the £150m allocated by the Department for Work and Pensions for discretionary housing payments (DHPs) over the past year.
DWP figures show that, in 2016/17, nearly two thirds of councils failed to spend all the money that was available to them and eight councils spent less than half.
The top under-spender in cash terms was Sunderland, which spent just £377,000 (or 42%) of the £897,000 at its disposal.
Other significant under-spenders included North Lincolnshire, which spent 17% of the £295,000 it was allocated, and North East Lincolnshire, which only spent one third of its £348,000 allocation.
The largest under-spender in London was Wandsworth, which spent just over £1m of its £1.2m allocation, meaning it failed to award 18% of the money on offer.
If councils fail to spend their allocations, the money remains with the DWP.
Sunderland says its failure to spend more than half of its allocation was due to a change in policy that saw it reducing the number of long-term claimants who receive DHPs year after year.
Since 2016, people awarded DHPs have been required to give more information about their financial circumstances and outline steps they are taking to increase their income.
Last year, councils nationally awarded DHPs worth a total of £183m, up from £163m in 2015/16, but down from the £199m paid out the previous year.
The payments are available to tenants with social or private landlords.
To quality, households must receive housing benefit or universal credit and demonstrate they face short-term financial hardship.
It is up to councils to decide how much a household receives and the length of time DHPs are paid.
They cannot be used for rent arrears.
Total underspend on DHPs in 2016/17 was £7.2m, up from £4.8m the previous year, but similar to the £7.7m councils failed to spend in 2014/15.
DWP analysis of DHP spending in 2016/17 shows that 124 councils spent over and above their DHP allocation.
This includes most councils in Scotland, where the Scottish government provided local authorities with a further £36.5m.
Outside Scotland, councils spent an extra £4.4m from their own budgets, down from £6.9m the previous year.
These include Croydon, which topped up its allocation by £500,000, taking its total spending on DHPs last year to nearly £2m.
There, awarding DHPs is seen as more cost effective than allowing families to become homeless and placing them in bed and breakfast accommodation.
DWP figures show the bedroom tax accounted for about half of DHPs awarded last year, with 10% resulting from LHA caps and 18% from the household benefit cap.
This cap, previously £26,000 per year, was reduced from November 2016 to £20,000 for families outside London (£23,000 in London).
The DWP says councils’ allocations are decided by ‘local factors’, with any underspend the previous year taken into account.