The oil major rose more than 1% or 4.8p to 437.2p after a US federal appeals court ordered tighter rules on compensation to help stem bogus or inflated claims for damages by businesses.
Upbeat figures from the powerhouse Chinese economy also helped the wider FTSE 100 Index steady after falls in the previous session, up 11.5 points to 6449.
A report showed that China's services sector expanded to a six-month high in August, but markets remain cautious with no breakthrough in sight on budget negotiations and warnings from Barack Obama to Wall Street over the risk of America defaulting.
While London investors held their nerve over the crisis, Germany's Dax and France's Cac 40 fell, partly on profit taking as the single currency climbed against the dollar.
Worries took their toll on Wall Street, with the Dow Jones Industrial Average down by more than 1% by the close in London. Sterling failed to advance on previous highs, despite buoyant economic data showing the services sector had its best quarter for 16 years.
Surveys this week, also including construction and manufacturing figures, showed strong performances across the board, but also indicated growth slowing down a little.
It was enough for currency traders to take profits on the pound, which slipped a cent against the greenback to just under $1.62 and also by a cent against the single currency, to a little below €1.19.
In equities, insurer Aviva helped the FTSE 100 to hold its course, after it completed the sale of its US arm to Athene Holding, fetching $800 million (£493m) more than expected. Shares rose 5.6p to 413.1p.
In other corporate news, budget airline easyJet said full-year profits were set to be at the top end of City expectations: the second hike to guidance in less than three months.
Shares initially rose as much as 2%, but later lost ground, down 6p to 1308p.
Discount retailer Sports Direct International was among the biggest top-flight fallers after the company's chief executive Dave Forsey and finance director Bob Mellors took up bonus scheme options to buy a million shares each, and immediately sold 950,000 each.
The move raised nearly £6.5 million each for the pair, but left shares in the group 10.5p lower at 698p.
The biggest risers on the FTSE 100 were Unilever, up 48p to 2367p, Tesco up 7p to 365p, GlaxoSmithKline up 24.5p to 1571p and RSA Insurance up 1.7p to 119.9p.
The biggest fallers on the FTSE 100 were Vedanta Resources, down 31p to 1059p, Fresnillo down 25p to 910p, CRH down 30p to 1466p, and Anglo American down 30p to 1472.5p.