Mr Lilley has asked John Gummer, the Secretary of State for the Environment, to investigate such a move, which could theoretically save thousands of pounds in housing benefit, which covers housing costs in full.
It coincides with Mr Gummer's inquiry into alleged discrimination against two-parent families in the allocation of council homes.
Both moves stem in part from a ministerial belief that social security and housing rules encourage young women to become pregnant - in spite of the fact that the housing allocated to many mothers is often only bed-and-breakfast accommodation.
However, Mr Lilley has ruled out the idea floated last week of seeking a contribution from parents where young mothers claimed they had been thrown out, allowing them to jump to the top of the housing list.
But Mr Lilley's enthusiasm for hostels or shared accommodation might not result in substantial overall savings in public expenditure since many councils would be unwilling or unable to provide the accommodation out of existing budgets.
Spending on single parents has risen from pounds 2.4bn in 1981-82 to pounds 6bn in 1991-92 at constant prices, Alistair Burt, the social security minister, told MPs yesterday. But in the absence of more child care and nursery facilities there is little scope for substantial reductions in mothers' income support.
Mr Lilley gave an assurance yesterday that single mothers were not going to be penalised by the Government. Ministers appeared quietly satisfied, however, that a debate on the issue appeared to have taken off. Mr Gummer has already ordered a departmental inquiry into local authority rules covering the allocation of housing to single parents.
A speech at the weekend by John Redwood, the Thatcherite Secretary of State for Wales, was discounted by a Department of Social Security source yesterday as not reflecting Government policy.
Mr Lilley also delayed the publication, expected yesterday, of his projections of total social security spending until the end of the century. The projections, part of the spending review ordered by Michael Portillo, Chief Secretary to the Treasury, will be revealed later this week.
But both Mr Lilley and Mr Burt invoked the weekend statement by David Blunkett, Labour's health spokesman, as proof that ministers were right to tackle the issue of single parents. Mr Blunkett spoke of acceptance by fathers of their obligations towards their children and housing policies which did not encourage the belief that the only way to a home was having a baby. 'I agree with him,' Mr Lilley told MPs yesterday.
The campaign continued as Tom Sackville, the health under-secretary, blamed 'feminists' for encouraging women to have children outside marriage. But calling for an end to the 'persistent attacks', Ruth Ashton, general secretary of the Royal College of Midwives, said single mothers were being scapegoated as a forerunner to cutting benefits: 'Are we really expected to believe young women get pregnant so that they can get pounds 34.80 a week income support and spend their time in dreary bed-and-breakfast accommodation, as so many do?'Reuse content