The Council of Mortgage Lenders (CML) previously raised concerns that many more existing borrowers could find themselves trapped under the new rules.
The FSA has now altered its plans so that lenders would be able to "switch off" the requirements for existing borrowers who wanted to get a new mortgage for the same amount or less, provided they had a good repayment history.
The clampdown follows a period during the property boom when would-be buyers increasingly stretched their finances to get on the ladder.
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Lloyds Banking Group is cutting 3,000 jobs and shutting 200 branches as the lender braces for a cut in interest rates, it has announced.