The main index added 0.2% and outperformed the broader European market as BP gained 3.2%, providing the biggest boost to the index after the company's second-quarter profit topped estimates.
The mid-cap FTSE 250 edged 0.1% lower by 0735 GMT as a near 8% drop in Virgin Money-owner CYBG weighed.
British Gas parent Centrica, whose earnings have been hit by a national cap on energy prices, sank 10.6% to its lowest level in more than two decades as it slashed its dividend and said its chief executive would step down.
Fresnillo skidded 7.5% after its profit plunged by more than two-thirds in the first half of the year due to a drop in production and higher costs.
A mix of weaker sterling, which hit a more than 2-year low on Monday, and hopes that central banks will cut interest rates have put the FTSE 100 on track for its second straight month of gains, but fading hopes of an orderly Brexit under new Prime Minister Boris Johnson could weigh on markets.
"The mood music around Brexit has certainly changed in the last week or so, along with the tone of the message from the British government, which has become much more uncompromising," CMC Markets analyst Michael Hewson said.
Most blue-chip companies that book a major chunk of their earnings in U.S. dollars failed to capitalise on the pound's weakness, however, as they were weighed down by Reckitt's sharp losses.
The maker of Durex condom and Lysol disinfectant fell 3.7% after it cut its full-year revenue view and said a slowdown in demand for infant formula in the United States and China had hit second-quarter sales.
On the FTSE 250, CYBG slipped after it forecast net interest margin to be at the lower end of its earlier view and reported a dip in mortgage loans and margins in the third quarter.
British Airways owner IAG fell 1.5% on the main index, while its mid-cap peers Wizz Air and easyJet shed roughly 2% each, after Germany's Lufthansa warned of a challenging European market in the near term.