Cities have been "unfairly" burdened with supporting those fleeing war and destitution, while "whole swathes" of rural areas have refused to sign up to house even a single asylum, the Home Affairs Select Committee added.
They are pushing for an overhaul of the 'dispersal' scheme, under which councils sign up voluntarily to house asylum seekers, that would see local authorities who have taken none or small numbers forced to take more.
The call came in a report authored by the committee, who lamented that contractors had reported difficulties in finding enough accommodation.
They singled out an area including Mrs May's constituency of Maidenhead, in Berkshire, and criticised it for having housed no people waiting for their refugee status to be processed.
Their report said: "The dispersal system appears unfair, with whole swathes of the country never receiving a single asylum seeker.
"The majority are being moved into low-cost housing in urban areas such as Glasgow, Stoke, Cardiff and of course Middlesbrough, where the ratio is 1 asylum seeker per 137 people.
"However, on the data we have received, local authorities in areas such as Maidenhead, Lincoln and Warwick have housed none."
Committee Chair Keith Vaz said Britain may need to house as many as 50,000 asylum seekers by 2017.
Last month Immigration Minister James Brokenshire told the committee the Government is looking to expand the number of local authorities designated as dispersal areas.
The committee's wide-ranging report also said it was "clearly wrong" that accommodation for asylum seekers in Middlesbrough had doors that were painted a "predominant colour".
A furore erupted earlier this year after claims refugees living in the town were housed in properties all painted a single shade of red that made them easy targets for attack and abuse.
There was also controversy when it emerged that asylum seekers in Cardiff had to wear coloured wristbands in order to receive meals.
The committee welcomed moves to repaint the doors and end the use of wristbands.
Mr Vaz said: "The compulsory wearing of wrist bands and the infamous red doors demonstrate an unacceptable attitude towards vulnerable people."
Dr Lisa Doyle, of charity the Refugee Council, called on ministers to devise a better strategy to house asylum seekers, many of whom are fleeing the brutalist regime of Bashar Al-Assad in Syria.
"The Government clearly needs to re-evaluate the way it houses asylum seekers," she told the Press Association.
"It's an issue of vital importance: we're talking about the way we as a country look after the comparatively small number of people who have fled war, rape and persecution and have come here seeking safety.
"It shouldn't be beyond us to find appropriate accommodation in sufficient numbers across the UK."