Fabian Society research identifies shortfall in funding for 1.2 million older people.
Work and Pensions Secretary vowed to prioritise "any individuals whom we know from our systems to be terminally ill".
Lone-parents, disabled children and ethnic minorities will be among worst-hit, says EHRC.
Government agrees to keep system open for six more months after pressure from Labour.
Thinktank says 340,000 people could be taken out of poverty if Philip Hammond takes action.