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The bank, which is part of HSBC, said the withdrawal was to allow it to cope with the unprecedented demand for its range of mortgages.
First Direct said applications have been five times its usual levels.
Chris Pilling, chief executive of First Direct, said: "The flood of interest in our mortgages has meant we're taking longer than we'd like to handle applications, especially from non-customers.
"Rather than increase interest rates dramatically to discourage new applications, we've decided to withdraw temporarily from offering mortgages to non-customers until we've cleared the backlog."
"We want to be back in the market as soon as possible."