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Second-placed Hayes’ seven-game winning Kent League Premier Division streak ended at home to Blackheath on Saturday.
Blackheath totalled 227-7 from their 50 overs as Matthew Golding and Riley Ayre hit 71, Alfie Peck (3-49) best with the ball.
In response, Rory Low top scored with 37 but Kent’s Arafat Bhuiyan (4-20) helped to restrict Hayes to 102 all out in the 28th over.
That allowed Minster to extend their lead at the summit to 26 points thanks to a 24-run victory at Sandwich Town.
Kai Appleby blasted 100 off 75 balls in their 295 all out, with opening bowler Alex Smith (3-56) among the wickets.
With Sandwich 19-3 early on, wicketkeeper Ryan Davies’ 133 from 131 balls helped them recover well, only to still fall just short of their target. Opening bowler James Speer (4-46) completed a good individual all-round display in the field.
St Lawrence & Highland Court eased past Lordswood by seven wickets.
Joe Gordon top scored for the Medway team with 23 but they were skittled for 89 in the 26th over, opening bowlers Jamie Hemphrey (3-21) and Joseph Payne (3-39) both doing well.
In-form Will Hilton and Darren Stevens, unbeaten on 31 and 30 respectively, saw them across the line in the 14th over, despite South African overseas bowler Thando Ntini’s figures of 2-47.
Second-bottom Canterbury are now 10 points from safety after going down at home against Bexley.
Skipper Matthew Stiddard’s 76 steered Bexley to 241 all out while Italian overseas international all-rounder Anthony Mosca (4-35) again sparkled alongside Lewis White (4-45).
Jarred Lysaught then top scored, offering 40, but Canterbury were all out for 194 in the 45th over. Opening bowler Freddie Foster returned figures of 4-35.
Tunbridge Wells earned a four-wicket win against basement boys Bickley Park, who are seven points adrift of Canterbury.
Opening batsman Cam Hawkins’ 67 guided Park towards 173 all out, Govind Nair (4-30) doing well.
Ollie Morgan saw Tunbridge Wells to victory with 49 not out, despite Ranjit Singh’s figures of 2-44 from 10 overs for Bickley Park.