Chris Woakes Stuart Broad and Ben Stokes help out as the tourists struggle second time around.
Mark Wood finished the job.
County cricket returned to England on Saturday.
Clarke wants Surrey, who were due to welcome 2,500 fans into Kia Oval this weekend, to honour Bob Willis by winning the competition named after him.
The campaign was meant to start in April.
Broad is the second Englishman to reach the milestone and seventh bowler overall.
The 34-year-old has put himself alongside greats of the game by reaching 500 Test wickets.
The 34-year-old is on 499 Test wickets.
Penultimate day of match against West Indies at Emirates Old Trafford is washed out.