@Aaaabbbcccc
Someone educate me - if your income is so low that this is a real dilemma surely you get benefits/allowances so you can have both. This is a genuine question.
There are some individuals who don't because they can sometimes literally be £1-2 pounds over some threshold.
Depending on where you live in the UK, and the type of housing, you might have substantially different fuel bills while having roughly the same income. The welfare system doesn't take account of this.
Despite the publicity about wealthy pensioners, a substantial number of women who took time out from their careers to care for children or went part-time to care for parents or other family members, don't have much of a pension and inadequate resources to buffer them against financial shocks like this.
Tenants in private housing have their housing costs pegged to the Local Housing Allowance and it can be significantly out of step with their actual rent.
Universal Credit is capped for a large number of people. People with disabilities on legacy benefits didn't qualify for the UC uplift when it was available.
The Resolution Foundation, the Joseph Rowntree Trust and many others, including the Royal Society, have lots of relevant reports.