The oil giant set the pace with a rise of nearly 3 per cent, up 66.5p to 2555.5p, after it said an increase in production helped second quarter earnings more than double from a year earlier to $5.15 billion (£3 billion).
The firm also cheered investors by pledging to return more than $30 billion to them over two years.
But the FTSE 100 fell 43.3 points to 6730.1, after US figures showed that mortgage approvals fell to lower levels than a year ago, suggesting the US economic recovery is still tentative.
Sentiment was hit by a further drop in eurozone inflation to just 0.4 per cent, while investors were also nervous about the impact that sanctions on Russia could have on company profits.
Amid the gloomy data the pound slipped against the dollar, at 1.69, but held steady against the euro, at 1.26.
And in the banking sector, nerves were fuelled by a plunge in shares in troubled Portuguese bank Banco Espirito Santo after it reported a record half-year loss of 3.58 billion euros (£2.8 billion).
Lloyds Banking Group was down nearly 3 per cent - reversing an initial 1 per cent rise - after it reported lower profits of £863 million for the first six months of this year. The state-backed lender was impacted by £1.1 billion of legacy costs, including another £600 million to cover the mis-selling of payment protection insurance.
Even though the bank remains on track to restart dividend payments next year, shares fell by 2.2p to 74.3p. Royal Bank of Scotland was 7.6p lower at 355.3p and Barclays dipped 2.7p to 225.7p.
BG Group was 8.5p higher at 1172p - a rise of almost 1 per cent - amid relief that it avoided further shocks for investors in its second quarter update.
The group, which has been hit by downgrades caused by disruption in Egypt, reported a 25 per cent rise in profits to $1.37 billion.
Another rise in the wake of results included BT with a gain of 0.6p to 388.5p, although Guinness drinks giant Diageo slipped 3p to 1786p after its full-year figures.
Away from corporate results, shares in Balfour Beatty fell almost 6 per cent or 14.8p to 237.9p after it announced it had terminated merger discussions with Carillion.
Balfour was unhappy that Carillion - off 18.9p to 334.3p - had made the "wholly unexpected" request to include Balfour's US business Parsons Brinckerhoff as part of the merger discussions.
However, Balfour shares recovered some of their earlier 6 per cent decline after Carillion said it remained keen on a tie-up.
The biggest risers on the FTSE 100 were Royal Dutch Shell up 66.5p at 2555.5p, Intu Properties up 8.5p at 328.8p and ITV up 4.2p at 208.8p. The biggest fallers were Schroders down 109p at 2390p, Weir Group down 101p at 2567p and St James's Place down 28.5p at 726.5p.