The liquidators of Stanford International Bank argued HSBC missed "warning signs" that the Antigua-based lender was a fraud before it ultimately collapsed in February 2009.
In 2012, Stanford was sentenced to 110 years in prison in the United States for running a $7 billion Ponzi scheme affecting approximately 18,000 former investors.
Prosecutors said Stanford sold fraudulent high-yielding certificates of deposit through Stanford International Bank and used investor money to make risky investments and fund a lavish lifestyle in the Caribbean.
The liquidators brought a civil case in London to recover 116 million pounds which was paid out of Stanford International Bank's accounts with HSBC, before being paid to Stanford International Bank's customers in redemption payments and interest.
Their lawsuit was thrown out by the Court of Appeal last year and, on Wednesday, the United Kingdom's Supreme Court dismissed the liquidators' appeal by a four-to-one majority.
Announcing the court's decision, Judge Vivien Rose said the payments "do not amount to a recoverable loss because the payments made relieved Stanford International Bank of 116 million pounds' worth of its contractual liabilities".
She added that the bank's assets would have been the same if the payments were not made because "it would have 116 million pounds more in cash but it (would have) owed 116 million pounds more in debt".
An HSBC spokesperson said in a statement: "HSBC is pleased with the result but there is no further comment."
(Reporting by Sam Tobin; Editing by Mark Potter)
