Storm shared the overnight lead with Jose-Filipe Lima after both fired record rounds on Thursday. Their first-round 65s were bested by four players on Friday, but Storm's 67 put him at 12-under-par 132 for a one-shot lead heading into the weekend.
The new San Roque Club Old Course record now belongs to Robert Karlsson, who fired a 9-under 63 in the second round to jump from 48th place into a tie for second at 11-under-par 133. Karlsson's round included a hole-in-one at the 193-yard, par-3 fourth.
Joining Karlsson in second place were Carl Suneson (64), John Bickerton (65), David Griffiths (65) and Titch Moore (67). In that group, only Moore's score would not have broken or tied the previous course record.
Thomas Bjorn (64) and Fredrik Widmark (65) also went low in the second round to move into a tie for seventh place with Jose Manuel Lara (66) at minus-10.
Storm, 28, played his first nine holes -- the back nine -- at even-par after a birdie at the par-4 12th and a bogey at the par-4 15th.
The 1999 British Amateur Champion birdied the first two holes on the front nine for the second day in a row to reach 9-under, then finished off his 67 with three straight birdies to end his round.
Since his British Amateur victory seven years ago, Storm has not performed up to expectations. This weekend he leads for the first time after two rounds, and will be going for his first professional win.
'I think most people thought as British Amateur Champion you should go on to great things, but it takes a lot of hard work and dedication,' Storm said. 'And maybe I made too many changes when I turned pro.'
Storm's best finishes this season came at the Malaysian Open, where he tied for eighth, and the Qatar Masters, where he finished alone in eighth. Last year, he tied for second place at the European Open.
'Finishing second in the European Open was massive for me,' said Storm, who lost his tour card in 2002, 'more financially than anything.'
Niclas Fasth and Louis Oosthuizen are three shots off the pace at 9-under and in 10th place. Defending champion Peter Hanson shot a 69 and leads a group of nine players tied for 12th place at minus-8.
Among those who share 12th with Hanson are eight-time Order of Merit winner Colin Montgomerie, amateur Jordi Garcia del Moral and David Bransdon, who carded a hole-in-one at the 225-yard eighth.
Raul Ballesteros -- the nephew of five-time major champion Seve Ballesteros -- finished four shots better than the cut line at 7-under after a 71. Ballesteros is playing on a sponsor's invitation.
Lima shot a 1-over 73 in his second round to tumble into a tie for 26th place at minus-6.