Strong winds prevented any play before 1pm, but the 45-year-old Welshman then moved onto the 10-under halfway total of 134.
He is one ahead of Spaniard Jose Manuel Lara overnight, although the round has still to be completed.
Morley’s Danny Denison enjoyed a fine second round, hitting 66 to leave himself just five shots off the overnight lead.
Hull’s Richard Finch, meanwhile, may struggle to make the cut after a round of 70 left him one over, 11 shots behind leader Price.
First-day leader Damien McGrane managed only five holes and parred them all to remain seven under.
Italian teenager Matteo Manassero, needing to win to have a chance of climbing into the world’s top 50 and qualifying for the Masters, is five behind following a 71.
Robert Rock wrote off his chances of making it to Augusta with a top-two finish when he had a septuple bogey 11 for an opening 77, but the Abu Dhabi winner shot 68 on his return – even with a seven on his card – and on one over is just inside the expected cut mark.
Price – forever remembered for his victory over Phil Mickelson at the Belfry a decade ago – has not finished among Europe’s top 100 money-winners since 2004 and last season held onto his card by little more than £1,000. Helped by holing a bunker shot on the short 16th, Price had six birdies and did not drop a stroke all day.
“I’m delighted with that,” he said.
“It’s been a long time since I’ve been anywhere near a leaderboard. It’s nice to be up there.”