Englishman Fitzpatrick, 21, started the day at the top of the leaderboard on his own and a two-under-par 69 gave him a nine-under total of 133, the same as experienced Dane Kjeldsen (68).
The pair were one stroke in front of Thailand's Kiradech Aphibarnrat (67) and Richard Bland of England (67) after another warm, autumnal day at Woburn.
Fitzpatrick, aiming to become the youngest-ever winner of the $4.55 million event, was unable to repeat his swashbuckling opening-day 64 and admitted there were times when he simply had to "grind" his way round.
"I felt like I struggled a little bit out there today," he told reporters. "I hit some bad shots on my back nine but managed to make some nice putts."
The former world amateur number one was thankful for a chip-in birdie at the third hole, his 12th.
"The fact it went in was a bonus," said Fitzpatrick. "I would have been happy just to get it up and down, it was a good little shot."
Co-incidentally, the 40-year-old Kjeldsen also had a chip-in birdie at the third where he holed out from a greenside bunker.
GRITTY COMPETITOR
"That set me up for the back nine," said the winner of the Irish Open in May. "I played well after that."
Kjeldsen, who also began his round at the 10th, followed up with birdies at the fifth and sixth before signing off with three straight pars.
The Dane has four previous victories to his credit and has earned a reputation as a gritty competitor.
Kjeldsen never likes to look too far ahead and was not even aware he had plotted his way to the top of the leaderboard.
"I haven't looked at any other results, I didn't even know I was leading," he said. "I just want to keep doing what I'm doing... going through the process and hitting some nice shots."
Ireland's Shane Lowry, winner of the WGC-Bridgestone Invitational in Ohio in August, was handily placed on seven-under 135 while 2010 U.S. Open champion Graeme McDowell was two strokes further back.
Tournament host Ian Poulter and triple major winner Padraig Harrington were back on 138, one ahead of former world number ones Lee Westwood and Luke Donald.
Dane Thorbjorn Olesen, who lifted the Dunhill Links Championship trophy at St Andrews last week, and Ryder Cup captain Darren Clarke were among the casualties of the halfway cut.
(Editing by Toby Davis and Pritha Sarkar)
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