* Europe's central banks follow Fed in leaving policy unchanged
* Official Chinese data and euro zone PMIs point to growth
* Dollar up from 6-week lows as euro dips
* European shares higher, oil near $109 a barrel
By Richard Hubbard
LONDON, Aug 1 (Reuters) - World shares, the dollar and oil all rose on Thursday after central banks in Europe joined the U.S. Federal Reserve in leaving policy unchanged to support a tentative recovery in the global economy.
The European Central Bank and the Bank of England both ended their latest policy meetings by leaving rates at record lows, a day after the Fed said the U.S. economy still needed its support and avoided any mention of a change to its stimulus programme.
The promise of abundant liquidity came as data for July revealed industrial activity picking up in the euro zone for the first time in two years, greater stability in China's vast factory sector and a surge in British production.
"They (central banks) want to keep the monetary conditions that are currently pretty accommodative in place to ensure the recovery continues," said ING economist James Knightley.
A report on U.S. manufacturing activity due later is also expected to show a modest rate of growth, building on the positive performance by the U.S. economy revealed in second quarter GDP data on Wednesday.
The better outlook encouraged investors back into riskier assets, lifting MSCI's world equity index 0.4 percent, sparking a rally in major euro zone government bonds and sending Brent oil up over $1 a barrel near $109.
U.S. stock index futures signalled that Wall Street would head higher as well with hopes rising that Friday's key July payrolls report will point to another solid rise in jobs.
However, traders said a strong employment report would increase the likelihood the Fed could begin scaling back its stimulus in September - a move that could hurt the gains in equities and commodities though it would support the dollar.
"We're very much looking for the dollar to continue to gain support, given the heightened expectations for non-farm payrolls, which are centred around the 200,000 mark," said Ian Stannard, head of European FX strategy at Morgan Stanley.
Employment outside the farming sector is seen rising by 184,000 during July, according to economists polled by Reuters.
The dollar index, which tracks the greenback's performance against a basket of major currencies, gained 0.7 percent to 82.02, though still not far from a six-week low touched on Wednesday after the Fed's policy announcement.
The euro had slipped 0.5 percent to trade around $1.3240 , off Wednesday's six-week high of $1.3345.
The encouraging Chinese manufacturing data, along with some strong corporate earnings and central bank actions, combined to lift European shares 0.8 percent by late morning to near a one-week high.
The STOXX Europe 600 Basic Resources index of mostly mining shares was among the big gainers, climbing 2 percent, while bank stocks jumped 1.6 percent after France's Societe Generale said its second-quarter earnings had more than doubled.
Earlier, after the improvement in China's official industrial activity survey eased concerns of a sharp slowdown in the world's second largest economy, Japan's Nikkei to jump 2.5 percent for its biggest one-day gain in three weeks.
Asian shares tracked by MSCI's Asia-Pacific ex-Japan index were more subdued though, adding 0.3 percent to snap a three-day losing run, while a rival report from HSBC showed factory activity in China running at its lowest in nearly a year.
In the fixed income markets, euro zone government bonds enjoyed solid demand thanks to the central bank's commitment to low rates, including in Italy and Spain where political risk was reaching crunch point.
"What we are still seeing here is the impact of the Fed statement. Basically what it says is that (the) probability of tapering starting in December has increased versus September, so an overall dovish statement by the Fed," Elwin de Groot, senior market economist at Rabobank said.
Ten-year German yields fell 6.8 basis points to 1.61 percent and yields on bonds issued by other highly-rated euro zone countries, including Austria, France, Belgium and the Netherlands, fell by about 5 to 6 basis points.
Equivalent Spanish yields were 2.5 bps lower at 4.60 percent as Spain sold bonds, while Italian 10-year debt fell 4 bps to 4.38 percent.