That is the proposal in a report from the International Longevity Centre and Cass Business School, part of City University London. The aim is to help low income pensioners use housing wealth for regular income.
The bank would be carefully targeted at older retirees who own their own homes and live alone but are income poor.
The authors suggest that, after receiving the appropriate financial advice, an individual sells a portion of their home to the state in return for a guaranteed lifetime income.

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Upon death the property would be sold, the debt to the state paid and any remaining value passed to the person's estate.
The report points out that housing equity owned by the population aged 65+ is estimated to be worth around £1.4 trillion or, £122,000 per person on average. In households with a deceased partner, home equity could be twice this average. Around 40,000 new people each year could benefit from the scheme.
The bank would sit along-side and not replace existing commercial products.
Launching the paper, Professor Les Mayhew, said: "The proposed recent pension reforms, whilst welcome, do not address the needs of existing pensioners whose incomes are fixed and therefore unaffected.
"Its main purpose would be to improve living standards in retirement, as well as making more money available for every day tasks and services such as help around the home, home maintenance, holidays, etc.
"The proposal is aimed at a sizeable group of older home owners, perhaps as many as 400,000, who have relatively small incomes of, say, £15,000 per annum or less, consisting mainly of the state pension and limited additional sources."
Baroness Sally Greengross, chief executive of ILC-UK, added: "The value stored in people's homes could be used to provide greater income in old age and improve living standards.
"Whilst some people will chose to downsize, there is a large group of older people on low incomes for whom moving house would be impractical but for whom a higher income could significantly help improve their day to day life. "Traditional equity release schemes may not work for this group of the population and new ideas, like the Equity Bank, deserve serious consideration from Government and the financial services industry."