This was a leap of 22% from February's lending figure of £25.5 billion and is 10% higher than the £28.3 billion of lending reached in March last year.
CML director-general Michael Coogan said: "This is the highest-ever March lending figure. It is clear that many borrowers are taking sensible steps to shelter against higher mortgage costs. There is still a question mark over just how strong mortgage lending will be over the coming months as the prospect of higher interest rates takes its toll on demand. But, we continue to expect mortgage lending to reach a record £360 billion this year."