* Sterling strengthens against dollar, euro
* U.S., euro zone manufacturing data disappoints
* Investors await UK Q2 GDP data on Wednesday
LONDON, July 24 (Reuters) - Sterling firmed against the euro and the dollar on Tuesday after weak manufacturing data in the euro zone and the United States, though investors were cautious before Wednesday's second quarter UK economic output data.
The euro zone's private sector shrank for a sixth successive month in July, according to purchasing manager data, making it increasingly likely the bloc will slide back into recession, while U.S. manufacturing activity expanded at its slowest pace since late 2010.
This helped the pound gain 0.15 percent to $1.5582, with traders citing commercial demand from the Middle East.
Against a euro also dented by concerns Spain may need a full bailout, sterling strengthened 0.4 percent to 77.85 pence per euro, taking it close to a more than 3-1/2 year high of 77.56 pence touched on Monday.
But analysts warned consistently negative data coming from most developed countries could push investors, worried about stalled economic growth, back towards safer currencies, which would hurt sterling against the likes of the dollar and yen.
"Now the PMIs have come out lower than expected and BBA mortgage approvals were also lower in the UK, I expect we'll see further dollar strength," said Craig Erlam, market analyst at Alpari. "I think the next support level will actually be $1.5437, followed by the July 12 low of $1.5393."
On Wednesday, the pound could be vulnerable as the focus switches back to the UK economy.
Economists predict the first estimate of second quarter GDP will show a 0.2 percent quarter-on-quarter contraction, which would extend Britain's recession into a third quarter.
Analysts said the estimated 0.2 percent decline was already priced into the market, but warned more disappointing numbers could see the pound sell off.
UK data recently has pointed to a weakening UK economy. Figures from the British Bankers' Association on Tuesday showed mortgage approvals in Britain were 21 percent lower on the year in June.
"Potential data disappointments tomorrow could add to the headwinds for sterling against safe-haven currencies like the dollar and Japanese yen," said analysts at CitiFX in a client note, adding that they see a deeper 0.3 percent quarterly deterioration.
"The headwinds could intensify further if investor concerns about the euro zone grow into broader risk sell-off across the board."
Sterling has lost ground against most currencies since late last week, hitting a seven-week low against the yen of 120.98 yen on Tuesday, according to Reuters data.
Although it remains vulnerable to deepening worries over Spain and Greece's debt problems, analysts predicted the pound could touch new multi-year highs against the euro.
"We're still of the view that euro/sterling will grind a little bit lower, in line with euro weakness," said Peter Kinsella, currency strategist at Commerzbank. (Editing by Nigel Stephenson)