Councils will be able to draw upon a £4m fund to cover the bill for giving residents a rebate while they are out of their homes.
The councils will not be forced to introduce the payment exemptions, Number 10 said.
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He is accused of raudulently attempting to gain money and housing by pretending he had lost family members.
A plan will be outlined on Monday by Northern Ireland Secretary James Brokenshire after the fourth deadline is missed.
The Government intends to fund abortions in England for women arriving from Northern Ireland, where it is illegal, Philip Hammond has said.