Webster and overnight leader Mark Foster, also of England, stand at 6-under-par 138 heading into the weekend, one stroke clear of Gregory Bourdy and Sam Little for first place.
Ian Garbutt is alone in fifth place at 4-under-par 140, and a group of six golfers share sixth place one stroke further back. The cut was set at plus-4, with 64 players failing to move on.
Webster, who began his round at 1-under-par, collected seven birdies Friday. He opened on the back nine with consecutive pars before a birdie at No. 12 put him at 2 under.
A two-time winner on tour, Webster bogeyed a pair of par-3s before heading to the front nine, but a birdie at the 16th helped him make the turn at minus-1. Consecutive birdies to start his second nine moved him to 3 under, and three more birdies in his final four holes gave him his share of the lead.
'My mind is pretty good on the course, so if I can keep that up, I know I can be there right in the end,' Webster said.
Webster has compiled 10 top-20 finishes so far this year, including his first European Tour win at the Telecom Italia Open in May. He will be in the field at the PGA Championship next week -- his first tournament in the United States, and only his second visit there after celebrating his 30th birthday in Las Vegas earlier this year.
'If I am playing well I will look forward to it,' Webster said. 'It is going to be difficult, but if I am playing well I will love it, I know I will.'
Foster opened his round with a bogey at the par-four first to fall to 3 under. He then strung together seven straight pars after that before a birdie at No. 9 moved him back to his overnight score of minus-4.
A birdie at the par-5 12th briefly put Foster at 5 under before he gave that stroke back with a bogey at No. 14. The 30-year-old Briton then rebounded with an eagle at the par-5 16th, knocking a 3-wood within 6 feet before making his putt to move to 6 under.
'The eagle on 16 was the highlight,' said Foster, who shot a 2-under 70 on Friday. 'I was playing fine but not much [was] happening. I just kept telling myself to hang in there.
'I said yesterday I wasn't going to worry about other people and [I] did my job out there today. Pleased with it.'
Bourdy briefly climbed to the top of the leaderboard at 7-under-par before a pair of late bogeys dropped him to minus-3 on the day and 5-under-par 139 for the tournament. Little posted a 68 to join Bourdy in second place.
Also posting a 68 in his second round was 1999 British Open champion Paul Lawrie, who is tied for 12th place at 2-under-par 142. Lawrie eagled his final hole -- the ninth -- to reach minus numbers.
'I am a far better player now than I was then (during his Open win in 1999),' said Lawrie. 'I hit far more good shots and quality shots than I used to. But my short game was mustard back then. I would like my short game of 1999 and long game of now. That would be a nice combination.'
Among those not making the cut was Marc Cayeux, who tied for third at last week's Scandinavian Masters. Cayeux finished at 10-over-par 154 after rounds of 78 and 76.
Also not making the weekend was Stephen Dodd, who ranks 10th on the European Tour Order of Merit. Dodd stumbled to a pair of 77s in his two rounds.