Jeremy Mogford, owner of the hotel and its excellent sister establishments, The Old Bank, Quod, and Gee's*, sponsors an annual short story competition in association with the Oxford Literary Festival; its theme is always food and drink, and this year's judges are Philip Pullman and Mary Berry.
You'll find full details here but to summarise, entries can be fiction or non-fiction, must be unpublished, and no longer than 2500 words. The closing date is 15th. January, 2017.
*I've stayed at or eaten in all these places often and recommend them most highly.