The Council of Mortgage Lenders said total lending jumped by 24% to £12.
2bn last month.
Meanwhile HM Revenue & Customs said completed sales rose from 64,000 in April to 71,000 in May.
In April property market activity slumped, after 1% stamp duty was reintroduced on 24 March on home purchases by first-time buyers, following a two-year exemption.
The CML warned that more big fluctuations in lending were likely to appear this year.
"Mortgage lending continues to seesaw, albeit against a broadly flat market," said the CML's chief economist Bob Pannell.
"Unfortunately, a number of one-off factors, such as the Diamond Jubilee and the Olympics, are set to distort market indicators over the coming months, and it may be the autumn before we can more accurately gauge the state of the market.
"Mark Harris, chief executive of mortgage broker SPF Private Clients, said: "May's uplift in lending is hugely encouraging given everything else that is going on at the moment with the eurozone crisis and a number of lenders reining back on their lending in response to this.
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