* UK May manufacturing PMI slips to 57.0 from 57.3 in April
* Mortgage approvals fall in April to lowest since July 2013
* Data points to continued output strength, cooler housing (Updates throughout)
By Ana Nicolaci da Costa and Andy Bruce
LONDON, June 2 (Reuters) - Britain's economic recovery is showing signs of a healthier balance after data on Monday suggested some of the heat is coming out of the housing market while manufacturing remains strong.
Mortgage approvals fell to a nine-month low in April, the Bank of England said, suggesting new measures to control mortgage lending were leaving their mark.
A separate survey showed that growth in the manufacturing sector dipped only slightly in May and was still robust.
"The UK's economic rebound looks an awful lot healthier after today's data, with more evidence that this is no credit-fuelled bubble," said Rob Wood, an economist at Berenberg bank.
But with business investment still lagging, Britain may struggle to move away from consumer-led growth any time soon.
Britain's surprisingly fast economic revival since last year has been driven largely by consumer spending and an upturn in the housing market, underpinned by record low interest rates.
Policymakers have long wanted to see a stronger contribution from manufacturing and business investment and the Bank of England has sounded increasingly concerned in recent weeks about the risk of the housing market overheating.
The BoE data showed lenders approved 62,918 mortgages in April, the fewest since last July and 17 percent below a six-year high in January. It was the third consecutive monthly slowdown and below the 64,750 forecast in a Reuters poll.
At the same time, the Markit/CIPS UK Manufacturing Purchasing Managers' Index (PMI) inched down in May to 57.0, as expected in a Reuters poll but stayed far above the 50 line that divides growth from contraction.
New orders piled in at a healthy rate and manufacturers took on more staff, albeit at a slightly slower pace than in April.
The BoE said on Monday that lending to non-financial businesses shrank by 2.4 billion pounds in April on top of a fall of 2.5 billion pounds in March. Lending to small businesses alone also contracted, down 0.6 billion pounds.
The data was unlikely to alter expectations that the BoE is likely to raise interest rates in the second quarter of 2015 and that it will try other measures to head off the risk of a bubble in the housing market, possibly as soon as this month.
Berenberg's Wood said "tighter mortgage regulations are more a speed bump than a road block for the housing market", where house prices have grown around 10 percent over the past year.
He said the rules would not end surging housing demand.
Options open to the BoE include making banks hold more capital against certain types of home loans or urging caps on how large mortgages can be compared to a borrower's income.
"While the slowdown in lending may persuade the FPC to refrain from taking action to cool the market, unless there is evidence that loan-to-income ratios are moderating some form of action will still be on the table," Matthew Pointon, property economist at Capital Economics said.
(Additional reporting and editing by William Schomberg; Editing by Ruth Pitchford)