It emerged that it was singled out by Mr Davey in a letter asking regulator Ofgem to examine whether the industry's profit margins for gas should be the subject of a market investigation.
The wider FTSE 100 Index climbed 19.9 points to 6591.6 over the course of the session but Centrica and rival SSE were among the fallers.
Mr Davey said there was evidence that British Gas had tended "to charge one of the highest prices over the past three years, and has been on average the most profitable".
Centrica shares were down nearly 2%, or 5.3p, to 308.9p, while rival SSE was off 6p to 1351p.
Centrica stock is now down by nearly a quarter since Ed Miliband's pledge last autumn to freeze bills if Labour won the next election.
Elsewhere, equities markets in Europe saw a mixed performance, with France's Cac 40 up and German's Dax down.
In New York, the Dow Jones was in negative territory.
On currency markets, the pound was flat at 1.64 US dollars and 1.20 euros.
Meanwhile in London, banking group Barclays announced its headline full-year profit figures a day early.
The stock market disclosure came after a report said that the bank was set to reveal a one-third fall in operating profits to £5.17 billion, while bottom-line profits should triple to £2.86bn.
Barclays, which was due to present its results today, confirmed that the figures were set to be £5.2bn and £2.9bn respectively.
Even though the underlying figure was below the City's consensus forecast of around £5.4bn, Barclays shares held on to earlier gains to stand 3.3p higher at 275p.
Elsewhere in the top flight, shares in Vodafone initially fell on speculation that it is preparing a seven billion euro (£5.8bn) bid for Spanish cable company Ono as it attempts to revive its European business, but it later recovered to finish flat at 222p.
The UK company is currently cash rich after the $130bn (£78bn) sale of its stake in US mobile phone operator Verizon Wireless.
Outside the FTSE 100, shares in set-top box maker Pace led the way in the FTSE 250 Index after Barclays improved its rating on the Yorkshire-based firm.
Shares rallied 27.7p to 385.5p, a rise of nearly 8%.
The biggest FTSE 100 risers were Fresnillo, up 70p to 862.5p, Petrofac up 37p to 1232p, Amec up 31p to 1073p and Randgold Resources ahead 106p to 4530p.
The biggest FTSE 100 fallers were Hargreaves Lansdown off 49p at 1304p, G4S down 6.1p to 229p, Babcock International down 25p to 1342p and Centrica down 5.3p to 308.9p.