How many horses have won the UK Epsom Derby on more than one occasion?

No horse can win the Epsom derby twice since only three-year-old horses are eligible.

The Epsom Derby originated at a celebration following the first running of the Oaks Stakes in 1779. A new race was planned, and it was decided that it should be named after either the host of the party, the 12th Earl of Derby, or one of his guests, Sir Charles Bunbury (the Bunbury Cup run at Newmarket would later be named in his honour). According to legend the decision was made by the toss of a coin, but it is probable that Bunbury, the Steward of the Jockey Club, deferred to his host. The inaugural running of the Derby was held on Thursday 4 May 1780. It was won by Diomed, a colt owned by Sir Charles Bunbury, who collected prize money of £1,065 15s.

The Derby Stakes, popularly known as The Derby, is a Group 1 flat horse race in England open to three-year-old thoroughbred colts and fillies. It is run at Epsom Downs Racecourse in Surrey over a distance of one mile, four furlongs and 10 yards (2,423 metres), on the first Saturday of June each year.

It is Britain's richest horse race, and the most prestigious of the five Classics. It is sometimes referred to as the "Blue Riband" of the turf. The race serves as the middle leg of the Triple Crown, preceded by the 2000 Guineas and followed by the St Leger, although the feat of winning all three is now rarely attempted.