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The match, described as a "closely fought game," saw both teams play well.
The first notable opportunity came from the visitors, with Luce's cross finding Lewis Townsend, but his header was comfortably saved by Rob Hannah.
Wrington had their chance when Lewis Chappell controlled a cross from Cam Milkins, only to see his shot narrowly miss the target.
Hannah made two excellent saves, keeping the score level, while Jack Hutchings created a chance for Chappell, whose shot was well saved by Pope.
The first half ended goalless after Rufeo Taylor missed a good opportunity for Ashcott.
The second half continued in the same vein, with both teams searching for a breakthrough.
Wrington's midfield trio of Milkins, Jake Marshman, and Marshall Hale dominated the first 15 minutes.
However, Ashcott gradually took control of the game.
The deadlock was broken when Josh Skuse's tackle on Taylor resulted in a penalty.
Henry Hutchings stepped up and sent Hannah the wrong way to score the only goal of the match.
Wrington tried hard to equalise but failed to create any clear chances.
Ollie Andrews was named the supporters' man of the match for his solid defensive performance and threat going forward.