The 35-year-old Welshman finished 36 holes at 11-under-par 133. Ian Poulter, who lives right down the road from Woburn in nearby Milton Keynes, was alone in second at 9-under 135 after a 5-under 67, while fellow Englishman Philip Golding shot a 67 of his own for third place at minus 8.
Price spread his scoring around Friday, picking up birdies at the second, fifth and seventh holes to go out in 33, before making his way home with birdies at the 10th, 13th, 17th and 18th.
Although Price hit only 13 of 18 greens in regulation Friday, as compared to 17 en route to his first-round 68, he made up for the discrepancy by taking only 25 putts in round two. Price totaled 31 putts on Thursday.
A two-time winner on the European Tour, Price expended a great deal of energy in 2001 trying to qualify for his first European Ryder Cup team. He earned the 10th and final automatic berth on the squad but has struggled a bit since his success, failing to finish in the top-10 through seven starts in 2002.
'I think two years ago I elevated myself to a good status in the game and I wanted to move on from there,' explained Price. 'However, I probably moved backwards and that's why I want to prove I am a top player, not just a middle-of-the-pack player.'
Poulter, whose triumph in the Italian Open two seasons ago helped him reel in the 2000 Rookie of the Year Award, added a second title six months later at the 2001 Moroccan Open. The 26-year-old is in a perfect state of mind to grab a third victory considering he can enjoy all the comforts of home this week.
'I've had Justin Rose, Steve Webster and Sam Walker all staying at various times this week. It's been like a hotel,' Poulter said. 'It's nice when you can sleep in your own bed and have others to come and stay, put their feet up and relax.'
Scotland's Sandy Lyle, winner of the 1985 British Open and the '88 Masters, and England's Simon Khan each turned in flawless 65s to pull within four shots of the lead. They finished alongside Soren Hansen of Denmark, who shot a 69, in fourth place at 7-under-par.
Defending champion Thomas Levet (70) and first-round co-leader Santiago Luna (71) were part of a group at 6-under. Trevor Immelman (67), European Ryder Cup captain Sam Torrance (68), 1998 British Masters champion Colin Montgomerie (69) and Rose (69) were among the players at minus 5.
A total of 88 players made the cut, which fell at even-par 144.
Thomas Bjorn withdrew three holes into Friday's round due to shin splints.
Full-field scores from the British Masters