Rolls shares revved up by 8 per cent or 82p to 1092p.
The wider London market was also in positive mood, climbing 29.6 points to 6808.1.
Bourses in Frankfurt and Paris made gains too though New York's Dow Jones Industrial Average edged into the red after making strong gains in the previous session.
It came after the US Federal Reserve signalled that interest rates would remain at record lows for longer.The pound soared to a near six-year high against the greenback as remarks by Fed chair Janet Yellen suggested the UK would be the first to hike the cost of borrowing.
Her comments, coupled with signals from the Bank of England that have prompted expectations of a rise by the end of 2014, saw sterling surpass 1.70 US dollars and beat a previous August 2009 peak to reach a level not seen since October 2008.
The pound was also slightly up against the single currency, at 1.25 euros.
Optimism over the UK recovery was boosted by the latest retail sales figures from the Office for National Statistics, which showed the sector is enjoying the longest period of sustained growth since before the recession.
Demand for UK-made goods also rose strongly in June, according to the latest CBI Industrial Trends Survey.
Mobile phone giant Vodafone led a shortened fallers' board after Bank of America Merrill Lynch said the near-term outlook in Europe for the group continued to be difficult. Shares were off 3.2p at 194.8p.
In contrast, BT rose 7.5p to 392.5p after regulator Ofcom outlined new requirements on the telecoms firm to promote competition among superfast broadband providers. Shares were higher as Ofcom also rejected a complaint from rival TalkTalk that BT had failed to maintain a sufficient margin between its wholesale and superfast-broadband retail prices. In corporate news, shares in transport group Go-Ahead rose after it said it expects its Southern, London Midland and Southeastern rail division to deliver operating profits ahead of previous expectations.
The improvement reflects lower energy costs and a better operational performance after its three rail franchises achieved growth in passenger journeys of between 4 per cent and 5 per cent.
Investec Securities kept its buy rating on the stock and increased its forecast for full-year pre-tax profits by 9.2 per cent to £83 million. Shares climbed 4 per cent or 86p to 2263p.
Rival operator Stagecoach was also up, lifting nearly 2 per cent or 6.3p to 373.8p after its Virgin Rail joint venture secured a new West Coast mainline franchise until March 2017.