The Financial Services Authority (FSA) estimated that the bank will have to pay Â£29.3 million in compensation to NHFA customers as well as the fine, which is the largest ever levied in retail banking.
According to the regulator, between 2005 and 2010 2,485 elderly customers were advised on making investments â but in a number of cases the advice was deemed unsuitable as the individualâs life expectancy was less than the recommended five-year investment period.
An independent review found that 87 per cent of customers were involved in an unsuitable sale, the FSA explained.
Tracey McDermott, acting director of enforcement and financial crime, said: "NHFA was trusted by its vulnerable and elderly customers. It breached that trust to sell them unsuitable products. This type of behaviour undermines confidence in the financial services sector.
"HSBC, who owned NHFA, has now recognised the issues and taken steps to do the right thing. They have been given credit for that - but for some customers it will be too late.â
In a statement, Brian Robertson, chief executive of HSBC, said: "I fully accept that NHFA failed to give suitable financial advice to some of their customers. This should not have happened and I am profoundly sorry that it did.â
HSBC agreed to settle at an early stage in the case which entitled the bank to a 30 per cent discount on the fine.
By Jim Ottewill