The CML attributed the surge in activity to the end of the stamp duty concession period.
Overall 51,200 loans were approved for house purchase in March at a value of £7.4bn and 28,200 loans were approved for remortgage at a value of £3.6bn.
First-time buyers accounted for 42% of total house purchase loans, the highest proportion since 2001.
By value first-time buyers took out loans worth £3bn up 76% from the previous month and 67% from March the previous year.
Of those first-time buyers taking out a mortgage in March, 63% bought a property valued between £125,000 and £250,000 so were exempt from stamp duty.
Although the stamp duty holiday only related to first-time buyers the CML said there was a tendency for property transactions to involve “chains” resulting in knock on effects to other house purchasers also.
Around 27,200 loans worth £4.3bn were taken out by home movers in March up by 25% compared to February and 19% by value.
Paul Smee, director general of the CML, said: “We expected this significant increase in borrowing for March because of the stamp duty holiday.
“If lending follows the same pattern as after previous stamp duty concessions we will likely see a drop in activity in the next few months.
“It will take some time before we can judge whether other initiatives such as the NewBuy scheme and the reinvigorated right to buy will compensate for this effect.”
Marta de Sousa, director of residential property developers, Lux Reality, said the stamp duty holiday caused a frenzy of activity but the fireworks won't last.
She said: "The market is set to fall back to earth with a bang. The barrier to entry is rising by the day and the banks are being extremely cautious when valuing properties.
"There's just too much uncertainty around mortgages, and it's making people sit on their hands.”
Meanwhile Paul Hunt, managing director of Phoebus Software, said: “While bunting and party hats would normally be in order following a 76% monthly rise in lending value to first-timers, March’s figures are the crest of a wave.
“April undoubtedly will show falls on a similar scale. We will see an apparently violent fall in lending next month, but these big fluctuations mask the true picture of ongoing steady progress in the lending market.”
