Less than a quarter of those on the Government's reduced benefits will be able to make up the shortfall by finding work or moving to cheaper accommodation.
Research carried out by the Carried out by the Centre for Economic and Social Inclusion (CESI) for the Local Government Association (LGA) shows that compared the financial impact on benefit capped recipients in a given area with the local job opportunities and potential to move into cheaper accommodation.
The study shows that by 2015/16 the income of households claiming benefit will be lower on average by £1,615 per year (£31 per week).
However, a shortage of jobs and affordable homes in many areas means that four out of every five of those households are likely to need some form of assistance from their council to help them cope with the reduction in welfare.
It is estimated that the combined impact of housing reforms on these tenants is likely to be £1 billion each year.
Yesterday the Government announced the final stage of the benefit cap nationally.
The LGA, which represents more than 370 local authorities in England and Wales, warned that the welfare reductions will syphon money away from local services such as caring for the vulnerable and elderly, fixing the roads and picking up the bins.
Cllr Sharon Taylor, Chair of the LGA's Finance Panel, said: "In many areas welfare reform is not encouraging people into work because the jobs simply don't exist, while the opportunities for people to downsize their homes to cope with reductions in benefits are severely limited by a lack of affordable accommodation.
"Unless more is done to create new jobs and homes, households will be pushed into financial hardship and we will see a huge rise in the number of people going to their councils asking for help to make ends meet."
The LGA has demanded three major policy initiatives:
1. Help councils deliver new homes by relaxing the rules which severely limit how much councils can borrow against their existing housing stock. Recent research shows that councils could build up to 60,000 new homes over the next five years if they were allowed to invest in housing under normal borrowing guidelines.
2. Give councils and their partners in business more influence over employment schemes so that training providers produce more people with skills that are closely matched to what employers in the area need.
3. Immediately re-evaluate the Discretionary Housing Payments (DHP) fund to ensure supply better matches demand in local areas. The scheme should be redesigned to ensure that the Government meets its responsibility.