This compares with £3.7bn in the first quarter of last year. Nearly half of the lending was for remortgage rather than house purchase.
By the end of March buy-to-let lending accounted for 13.4% of total outstanding mortgage lending in the UK - up from 13% the previous quarter and 12.9% at the end of the first quarter of 2012.
Paul Smee, CML director general, said: "The buy-to-let mortgage market is performing well, against a backdrop of robust landlord - and tenant - demand for good quality rental property.
“Loan performance compares favourably with the owner-occupier sector, and buy-to-let continues to grow as a proportion of the overall mortgage market.
"As the private rented sector looks likely to be the longer-term tenure in which more households may live in the future lenders are actively looking at how they can best evolve their future lending for those landlords who may wish to offer longer-term tenancies to their tenants - although concrete landlord demand for such borrowing is not yet clear."
There are now around 1.46m buy-to-let mortgages in the UK accounting for around 13% of the total estimated stock of 11.26m mortgages.
Of all mortgages in arrears of over three months only 8.3% were buy-to-let (down from 9.0% the previous quarter and 10.5% in the first quarter of last year).
The possession rate, at 0.11%, was higher in the buy-to-let sector than the 0.07% in the owner-occupied sector, but fell from its previous quarterly rate of 0.12%.
