Start by checking on the Local Housing Allowance rates for the area that your mother lives in:
https://lha-direct.voa.gov.uk/search.aspx
Then start looking for rental accommodation in that area, where the cost of renting isn't higher than (or is only marginally higher than) the LHA figure. (Try sites such as Rightmove, Zoopla, PrimeLocation, Gumtree, etc, as well as local newspapers, estate agencies and rental agents).
Get your mother to apply for Housing Benefit
https://www.gov.uk/housing-benefit
or Universal Credit, as appropriate
https://www.gov.uk/universal-credit
If your mother isn't already in receipt of Pension Credit, check to see if she's eligible:
https://www.gov.uk/pension-credit
When your mother's in her new home, check that she's claimed the automatic single-occupier discount on her Council Tax AND that she's enquired about the possibility of a further Council Tax reduction from her local authority:
https://www.gov.uk/apply-council-tax-reduction
Use a benefits calculator to see if there's any further support which she might be entitled to:
https://www.gov.uk/benefits-calculators