Cevaer shot 2-under-par 70 Saturday, while Singh managed a 1-under 71.
The field was hampered Saturday by gusty winds on the course at the London Golf Club.
"I was missing a lot of putts and it was windy," Singh, also a second-round co-leader, noted. "I said (to myself) 'just hang in there.' I had a shaky start, but I covered up with a good finish."
It is the third time in his career Singh has held at least a share of a third-round lead, while Cevaer had never previously held a 54-hole lead after Saturday play.
"I managed to strike a perfect drive (at the 18th hole)," Cevaer said. "That's brilliant for me."