Banbury have been handed a home draw but Wallingford must travel in the first round of the EHA Men's Cup next season.
Banbury have been drawn at home to Andover while Wallingford visit Gore Court, with ties taking place on September 23.
Oxford University, who were relegated from the National League last season, have been handed a bye into the second round.
OTHER CUP DRAWS
EHA Men's Trophy 1st round (Oct 21): City of Oxford v Old Williamsonians.
EHA Men's Vase 1st round (Oct 28): Abingdon v Fleet, Bicester v Trojans, Wallingford v Horley.
Women's Trophy 1st round (Oct 21): Henley v Barnes, West Witney v Wycombe Rye. Byes: Banbury, Oxford Hawks.
Women's Vase. 1st round byes: City of Oxford, Wallingford.
Men's Veterans Cup 1st round (Nov 11): Reading v City of Oxford, Wallingford v Aylesbury.
Men's Vintage Cup 1st round (Nov 4): Ben Rhydding v Oxford Hawks, City of Oxford v Bowdon.
Timpson Trophy 1st round (Jan 27): Banbury v Bromley.
Girls' Under 15 Cup 1st round (by Sep 30): Sir William Borlase's GS, Marlow v St Edwards School, Wallingford School v Chesham High School. Byes: Burford School, West Witney HC.
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