RBS gained 2% on news of its withdrawal from the state-backed Asset Protection Scheme (APS) in another buoyant day for the FTSE 100 Index, which closed 40.4 points higher at 5910.9 after yesterday's 1% gain.
Trading was more subdued on Wall Street's Dow Jones Industrial Average, which was down 10 points as the Footsie closed following lower-than-expected third quarter figures from technology giants IBM and Intel.
Spirits were lifted in Europe after Moody's decided against downgrading Spain to junk status. Analysts expect the country will soon make a request for help to Europe's bailout fund, which is a necessary condition for the European Central Bank to start buying its bonds in the markets.
Job figures in the UK also exceeded expectations, with jobless claims falling by 4,000 and unemployment dropping to 7.9%. Employment grew in the quarter to August to 29.6 million, the highest since records began in 1971, although part-time employment made up a larger portion of the figure.
And the pound was given another reason to strengthen against the euro and dollar after minutes of the Bank of England's most recent policy meeting offered signs that more quantitative easing in November was far from guaranteed.
Sterling rose to nearly 1.62 US dollars and 1.23 euros.
RBS, which is 80% owned by the taxpayer, was firmly in the spotlight after it said it would exit the APS tomorrow, saving it £1.4 million a day and paving its way to becoming a private company.
Shares in the bank rose 6.1p to 286.1p.
Among other blue-chip risers, Tesco surged nearly 3% after broker UBS upgraded its price target on the supermarket, which it said was on the path to stability in the UK. Shares lifted 8.4p to 316.3p.
Miners benefited from the improved market confidence, with Eurasian Natural Resources up by 7% - 23.8p to 352.2p - and Kazakhmys 51p stronger at 760p.
In a quiet session for corporate news, shares in Guinness and Smirnoff drinks firm Diageo fell nearly 1% after a second quarter trading update fuelled worries about its performance in Asia Pacific. Shares were down 14p to 1768.5p.
Elsewhere, tool and equipment provider Speedy Hire was lower despite it saying that recent trading had been in line with expectations. Underlying revenues were 5% higher, helped by its focus on regulated industries in the UK. Shares were off 0.8p at 30.25p.
FTSE 250 firm Cable & Wireless Communications added 4%, up 1.3p to 37.5p, after it said it was in talks to sell all of its 51% stake in a Macau telecom operator.
The biggest Footsie risers were Eurasian Natural Resources up 23.8p to 352.2p, Kazakhmys ahead 51p at 760p, Anglo American 96.5p higher at 1905.5p and Vedanta Resources up 48p to 1147p.
The biggest Footsie fallers were BAE Systems down 7.8p to 321.3p, Pearson off 26p to 1217p, Bunzl 18p lower at 1099p and Compass down 10.5p to 684p.