* FTSEurofirst 300 up 2.44 percent, biggest rise in 11 months * ECB, BoE stance boosts case for Europe over U.S. - ING IM * EuroSTOXX 50 breaks above 200-day moving average By Toni Vorobyova LONDON, July 4 (Reuters) - European stocks posted their biggest one-day jump in 11 months on Thursday after central banks in Britain and the euro zone signalled that, unlike the United States, they are in no hurry to unwind stimulus. The Bank of England, under new governor Mark Carney, surprised markets by saying investors had been too quick to price in future rises in interest rates. European Central Bank President Mario Draghi then said rates would remain low and might be cut further, while the exit from stimulus was very distant. The comments offered reassurance to equity markets spooked in recent weeks by signs that the U.S. Federal Reserve is for its part moving closer to scaling back stimulus. "That's clearly another tick in the box in favour of European equities relative to U.S. equities," said Patrick Moonen, senior equities strategist at ING Investment Management. "We closed the underweight (on European equities) a couple of days ago and the next step is to go overweight Europe versus the U.S., based on valuation, based on relative economic indicators and based on relative monetary policy." The FTSEurofirst 300 rallied 2.44 percent to 1,178.99 points - its biggest rise since August 2012. Britain's FTSE 100 climbed 3.1 percent to 6,421.67 points. The Euro zone's EuroSTOXX 50 benchmark gained 3 percent to 2,646.54 points with volumes at 104 percent of the 90-day daily average despite a U.S. public holiday. Banks - which are the most direct beneficiaries of ample central bank liquidity and access to cheap funds - were among the top performers, rising 3.8 percent. Areas which would benefit from stimulus-driven economic recovery, such as autos, basic resources and retailers also did very well, but the rally was broad-based with every sector in the black by more than 1 percent. A further boost came from Portugal, where the prime minister and his coalition partner were said to be making progress towards defusing a political crisis that had raised fresh questions about the durability of the euro zone. "As long as Portuguese bond yields start heading back down again and we don't see contagion into the rest of the periphery, my expectations is that Europe slowly gets better from here," said Alistair Gunn, fund manager at Jupiter. Implied volatility on EuroSTOXX 50 - a crude barometer of investor risk aversion - fell 5.8 percent. The rally took the EuroSTOXX 50 through technical resistance at its 200-day moving average. "It looks like the bulls are taking back control," said Chris Wright, technical analyst at Informa Global Markets.