Oxford have been drawn away to the winners of Cockfosters and Amersham in the Kingfisher Beer Cup first round next year.
Cockfosters are members of the Saracens Hertfordshire League, while Amersham play in the Morrant Thames Valley League.
Banbury are also on the road with a trip to Leicestershire County League side Lutterworth.
The ties are due to take place on Sunday, April 28.
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