Spaniard Jose Maria Olazabal shot a 65 in his second round and joined Wall in the lead at 11-under-par 133. The duo stands one stroke clear of Paul Casey, who carded his second straight 67 to reach minus-10 for the tournament.
World No. 5 Retief Goosen is just two strokes off the lead after a second-round 68. He shares fourth place with Marc Cayeux (69), Nick Dougherty (64) and David Lynn (67) at 9-under-par 135.
Defending champion Padraig Harrington was among the 59 players who finished outside the minus-2 cut line. Harrington followed his opening-round 75 with a 3-under 69, but finished at even par.
Past champions Steven Richardson (7 over) and Sandy Lyle (1 under) also missed the cut, as did world No. 27 Miguel Angel Jimenez (1 under).
Wall, whose lone European Tour victory came at the 2000 Alfred Dunhill Championship, began the day tied for 53rd place at minus-1. But he opened his spectacular round on the back nine with six consecutive birdies to reach 7 under.
'It was a lovely day out there for me,' said Wall, whose best finish in 24 European Tour events this year was a tie for 12th place at the The Celtic Manor Wales Open in June.
The 30-year-old added a birdie at No. 17 and finished the outward nine with a 29 to get within one of the lead around the turn. Wall then reached minus-9 with yet another birdie at the first, and after four straight pars, he took the outright lead with birdies at Nos. 6 and 7.
'It is so hard out there and it is such a tough course if you miss the fairways, but I managed to avoid doing that for most of the day,' said Wall. 'I have improved a lot in the last couple of years. My game feels twice as good as it has ever done and the reason for that is my brain.'
Olazabal, who titled at this event 17 years ago, was tied for 14th place at minus-4 after the first round. He began his day by playing the first four holes at 1 over par before stringing together four straight birdies from the fifth to reach minus-7.
The two-time Masters champion moved further into red numbers with birdies at the 10th and 13th, and tied Wall for the lead with birdies at Nos. 16 and 17.
Olazabal's best finish this season is a third-place tie behind Tiger Woods at the British Open, so a win in this tournament would go a long way towards his bid to make another Ryder Cup team.
'Everybody is eager to play in the Ryder Cup and I would love to be in it again...but if I don't make it, I'm not going to throw myself off a bridge,' said the 39-year-old.
Four-time champion and event co-sponsor Bernhard Langer (69) shares eighth place with Scott Drummond (68) at minus-8. U.S. Open champion Michael Campbell, the 2000 winner here, is tied for 35th place at minus-4 after a second-round 69.
Another former champion, Barry Lane, is tied for 17th place at 6 under after shooting an even-par 72 on Friday.