* BoE cuts rates, restarts bond buying to ease Brexit blow
* European, UK shares rise, Wall Street seen higher
* Sterling falls vs dollar and euro, core bond yields drop
* Dollar gains vs rivals, focus on Friday's U.S. jobs data
* Oil gives up gains as oversupply worries weigh on prices
By Nigel Stephenson
LONDON, Aug 4 (Reuters) - European shares rose, government bond yields fell and sterling weakened against the dollar and euro on Thursday after the Bank of England cut interest rates and restarted bond purchases in a bid to ease the economic hit from June's vote to leave the EU.
U.S. stock index futures ESc1 1YMc1 SPc1 also rose and were last up 0.2-0.3 percent, indicating Wall Street would open modestly higher.
The BoE cut its main rate by a quarter percentage point to a record low 0.25 percent, its first rate change since March 2009, and said it would buy 60 billion pounds of government debt, along with 10 billion of high-grade corporate debt.
The rate cut was widely expected but not the other measures.
Sterling GBP=D4 initially rose against the dollar but quickly fell to as low as $1.3112. It last traded at $1.3142, down 1.4 percent on the day. It lost 1.1 percent against the euro EURGBP= , with the single currency last at 84.67 pence.
"The Bank of England has hit a perfect 'High Five' at today's meeting, over-delivering against market expectations and bucking the recent trend of central banks disappointing," JP Morgan Asset Management portfolio manager, Nick Gartside, said.
Britain's blue-chip FTSE 100 index .FTSE was up 1.5 percent. It and the more UK-focused FTSE 250 index .FTMC both jumped after the BoE move. The pan-European STOXX index, which includes British companies, extended gains and was last up 0.8 percent, led higher by banks .SX7P .
European bank shares tumbled this week after stress tests on lenders increased concerns some would have to raise extra capital but stronger-than-expected earnings from some banks have since soothed investors' nerves.
For Reuters new Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
British government bond yields hit record lows GB10YT=RR , dragging down euro zone equivalents. German 10-year yields DE10YT=TWEB , the benchmark for borrowing costs across the bloc, were down 4 basis points at minus 0.14 percent, compared with minus 0.11 percent before the BoE move.
"It is not just in the euro zone or in Japan, but even here in Britain we have a situation where central banks have to keep easing to offset headwinds to the domestic and global economy," Rabobank strategist Matt Cairns said.
The European Central Bank has been buying government bonds since March 25 in a bid to lift euro zone inflation and growth.
The Bank of Japan has also been buying government debt a government fiscal stimulus package unveiled on Tuesday led some economists to speculate Japan would rely less on monetary policy to revive the economy.
The dollar index, which measures the greenback against a basket of major currencies, rose 0.2 percent .DXY . The euro EUR= fell 0.2 percent to $1.1134. The yen, however, gained 0.1 percent to 101.15 per dollar JPY= .
The U.S. currency's strength followed forecast-beating private sector employment data on Wednesday, which led to marginally increased expectations of a Federal Reserve interest rate rise by the end of the year.
Markets will look to Friday's monthly U.S. jobs report for further clues to the Fed outlook.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS rose 0.5 percent, led by gains in resource shares. Tokyo's Nikkei index .N225 ended a see-saw session up 1.1 percent on strong gains from financials and with the yen then weaker against the dollar.
In other markets, oil prices initially rose after data on Wednesday showed a steeper-than-expected decline in U.S. gasoline stocks but concerns about persistent oversupply saw those gains erased.
Brent crude LCOc1 , the international benchmark, dipped 20 cents a barrel to $42.90, having touched a low of $41.51 on Tuesday, its weakest since mid-April. U.S. crude CLc1 was all but flat at $40.78 a barrel.
Gold XAU= rose after the BoE decision and was last up 0.4 percent at $1,362 an ounce. ($1 = 0.7610 pounds)