Commenting on the statistics, the BSA's director general Adrian Coles said that the majority of the deposits may have been in the aftermath of problems at Northern Rock.
He added: "This is more than double the amount deposited in August, nearly three times the amount deposited in September last year, and nearly £1 billion higher than the previous record.
"With savers searching for the best home for their money, the wide range of attractive savings products that societies offer proved to be very competitive."
The release of the figures by the BSA was made after the Association of British Insurers' director general, Stephen Hadrill, claimed that the Northern Rock difficulties had brought protection of savings into "very sharp focus".
Mr Hadrill made the comments while urging politicians not to increase the guarantee limit to over £35,000.
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