This photo has just come to light and we’ve identified most of the Shoreham FC players and the manager. The cup is the Royal Irish Rifles (later Royal Ulster Rifes) Charity Cup that Shoreham won twice. In 1903 when the RUR final was played at the Oxen Field (Windlesham Gardens area) and again in 1906 when it was played at the Goldstone Ground. The background more matches the Oxen Field I think added to which the players look a few years younger in that photo than those of later years so the photo is likely to be the Oxen Field in 1903
Incidentally, Shoreham and Southwick supporters in those days really got on well together. During the 1890’s when playing at home to Southwick some Shoreham supporters would gather at the station until the opposing supporters arrived then fight with them all the way to the Oxen Field ground. After the match the fight was resumed on the return trip to the station. During one local derby match after Shoreham had scored the linesman was knocked out for flagging the goal as offside! Fair enough.