This is according to the latest Regulated Mortgage Survey data published today by the Council of Mortgage Lenders.
The £8.4bn of lending for house purchase accounted for 57% of all mortgage lending in May (by value), while remortgaging at £4 billion accounted for 27%, and other lending (including lifetime, buy-to-let and further advances) at £2.3 billion accounted for 16%.
The number of mortgages to first-time buyers in May reached 25,100 - 29% higher than in April and 42% higher than in May last year.
First-time buyers accounted for 45% of all loans for house purchase, similar to the levels of the past few months but considerably higher than the 38% seen on average since 2007.
The number of first-time buyer loans was the highest monthly figure since late 2007 and a marked contrast to the low point of just 8,500 loans in January 2009.
By value, first-time buyer lending reached £3.4 billion in May, up from £2.5 billion in April and £2.2 billion in May last year.
The CML also found that for some months there has been an increase in the number of first-time buyers entering the market with smaller deposits - this has now resulted in a shift in the average first-time buyer loan-to-value ratio rising to 83%, up from 81% in April and the highest ratio since November 2008.
First-time buyers are also typically borrowing more (£113,400 in May, on average, compared with £110,000 in April and £105,000 in May last year) and typically now have higher incomes (£35,700 in May, up from £33,500 in May last year). The age of the typical first-time buyer remained at 29.
The number of loans to home movers in May was up by 32% on April but by a more modest 4% compared with May last year. And, in contrast to the shift in first-time buyer loan profile, movers have experienced far less change in average loan size, income, or loan-to-value.
Paul Smee, director general of the Council of Mortgage Lenders, commented: "Although monthly lending is still running at far less than half its typical monthly level during the peak, there is no doubt that the mortgage market is firmly open for business. Both the borrowing appetite of first-time buyers and the availability of attractive mortgages for them have improved markedly since a year ago.
"What is interesting is that, in contrast to some recent assertions, this is happening in parallel with the strengthening buy-to-let market. It is perfectly possible for both the buy-to-let market and the first-time buyer market to improve at the same time, as the evidence clearly demonstrates.
"It is important that the supply of housing steps up, as increased housing supply is a crucial factor in ensuring that housing is affordable over the long term."
