* FTSEurofirst 300 and STOXX 600 up 3.7 percent
* European stocks back at levels seen in early June
* Banking stocks among top performers (ADVISORY - Follow European and UK stock markets in real time on the Reuters Live Markets blog on Eikon - see cpurl://apps.cp./cms/?pageId=livemarkets)
By Sudip Kar-Gupta
LONDON, June 20 (Reuters) - Top European shares indexes posted their biggest rallies since August on Monday, led by heavyweight banking stocks, as weekend opinion polls boosted expectations that Britain would vote to stay in the European Union.
The pan-European STOXX 600 and FTSEurofirst 300 indexes both rose 3.7 percent, the biggest one day gain for each index for ten-months. Both indexes moved back towards a level last seen earlier in June.
Markets recovered from three straight weeks of falls, as recent momentum for the campaign to "leave" the European Union showed signs of waning, sending sterling towards its biggest one-day gain in 7 years.
Three opinion polls on Saturday showed the "Remain" camp recovering some momentum, although the overall picture remained one of an evenly split electorate.
Britain is due to vote on its European Union membership on June 23. Opinion polls have been split, although bookmakers have given a greater probability towards Britain opting to stay in the EU, rather than leave in a "Brexit" scenario.
"If the UK votes to remain in the EU, there will clearly be a short term market rebound, especially given the weakness seen over the past two weeks," JP Morgan equity strategist Mislav Matejka said.
"This would potentially take the market back to the levels from beginning of June, when the Euro STOXX 50 was around 3,050 points," he said.
Royal Bank of Scotland and Lloyds rose by 7 percent and 5.1 percent respectively.
Italian bank UniCredit also rose 6.3 percent after a media report that it would name former industry minister Corrado Passera as its new chief executive.
The banking sector is highly geared into overall market moves and domestically focused banks, such as RBS and Lloyds, were among the hardest hit stocks last week when "Brexit" looked more likely.
Travel and leisure stocks posted their biggest one day gain in 6 years, with UK names such as Thomas Cook as much as 8.3 percent higher.
The sector in Britain was lifted by the rise in sterling, which would make summer travel cheaper for British customers.
Only 10 STOXX 600 companies were in negative territory, with precious metals miners slightly lower. Gold was hit by the "risk-on" sentiment.
In spite of Monday's rebound, several traders remained cautious, given the uncertainty around the referendum.
"I would not buy into this move up, and I would still look to take some risk off the table," said Rupert Baker, a European equity sales executive at Mirabaud Securities. (Editing by Toby Chopra)