Paul Broadhurst and Gregory Havret tied for third place at 9-under-par 135. Emanuele Canonica, Marcel Siem, Steve Webster, Simon Khan and Stuart Little followed at 8-under-par 136.
Finch rocketed out of the gate with an eagle at the par-5 first at Castello di Tolcinasco Golf Club. He added a birdie at the par-4 fourth after his approach stopped within 7 feet of the hole and picked up a birdie at the par-3 fifth to reach 7-under.
The Englishman found trouble with a bogey at the sixth, but he recovered with a birdie at the par-3 eighth. Finch converted a 5-foot birdie putt at the par-5 ninth and made it three in a row with a birdie at the par-4 10th.
He kept on rolling with a birdie at the par-5 12th and jumped to minus-11 with a birdie at the par-3 14th. Finch then dropped his tee shot inside 9 feet at the par-3 16th and drained the birdie try to secure the lead at the halfway point.
'It's a difficult golf course, but because it's in such good condition if you hit good shots you give yourself the chance to hole some putts,' said Finch, who established a new course record on Friday.
Dredge tallied a pair of birdies over his first nine holes and climbed to 8-under with a birdie at the 10th. He continued his climb up the leaderboard with a birdie at the 13th and made a push to match Finch starting with a birdie at the par-5 15th.
Dredge hit his tee shot to the fringe at the par-3 16th, but walked away with a birdie to get within one of the lead. The Welshman then birdied the par-4 17th to join Finch in first, but Dredge dropped a shot at the last to finish one shot back after a 66.
'I didn't hit the ball as well today, but the putter was red hot,' said Dredge. 'It is nice when the hole feels the size of a bucket. Just hit it towards it and it was going in. The short game was very good today and I made a lot of saves.'
Adam Groom posted a 68 to finish alone in 10th place at 7-under-par 137. David Lynn and Jose Manuel Carriles were one shot further back at 6-under-par 138.
Last year's winner Graeme McDowell won't be around on the weekend. McDowell, who opened with a 70, managed a 74 on Friday to finish one shot off the cut line at even-par 144. Other notables who missed the cut were Ignacio Garrido and Robert Karlsson.