Clarke shot his second consecutive 68 and Glover turned in an even-par 70 early Friday and, while they were sometimes tied, the field wasn't to keep pace.
First-round co-leader Thomas Bjorn had a 2-over 72 in the second round and is among a group of four tied for third at 3-under for the tournament.
Chad Campbell (68 Friday), Martin Kaymer (69) and Miguel Angel Jimenez (71) are tied with Bjorn and another six golfers, including Masters champion Charl Schwartzel (67) are at 2-under.
Tom Lewis, a 20-year-old amateur who tied Bjorn for Thursday's lead, shot 4-over 74 Friday and is 1-under for the tournament. He is among five players, including Phil Mickelson (69), who are three strokes off the lead.
The fickle British Open weather was relatively tame the first two rounds, but forecasters say that will change Saturday with winds in excess of 40 mph predicted. The question will be when will the weather hit -- early to affect those trying to catch the leaders or late when the leaders are on the course.
Friday's play at the Royal St. George's Golf Club was highlighted by Tom Watson's hole-in-one on the 178-yard sixth hole. Watson, who has won the event five times, hit a 4 iron that took one big hop and disappeared into the hole. He shot 70 Friday and is 2-over for the tournament.
The cut came in at 3-over. World No. 2-ranked Lee Westwood and Padraig Harrington, who won the British Open in 2007 and 2008, are at 4-over.