The bank took £4.3 billion in deposits during the first nine months of 2008, compared with £2.5 billion last year.
Abbey is owned by Santander, the Spanish giant which swooped to buy the ailing Alliance & Leicester and the savings business of nationalised Bradford & Bingley.
The deals give it around 1,300 UK high street branches and deposits of £116 billion - making it the country's third biggest deposit taker behind Royal Bank of Scotland and the soon-to-merge pair Lloyds TSB and Halifax Bank of Scotland.
Abbey chief executive Antonio Horta-Osorio said: "We had strong deposit inflows demonstrating that Abbey, backed by the strength of Santander, is regarded as a secure and trusted home for UK savings customers."
Abbey has not taken part in the Government's plans to pump billions of pounds into ailing banks, as it has capital resources "well in excess" of regulatory requirements.
About 60% of the bank's balance sheet comes from customer deposits, with less than 10% of funding depending on volatile wholesale markets.
Santander injected £1 billion of its own funds into Abbey following the turmoil, which Abbey said had "profoundly changed the landscape for UK banking".
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