The Times shows various hits for a Miss Annie Luker who was a diver at the Royal Aquarium in Westminster - 1894-1901 period (the Royal Aquarium closed sometime soon after this - last night according to the google search Geoff mentions was 10 Jan 1903, and Annie was still there then), sometimes described as 'champion lady diver'. However, women were not allowed to participate in 1896, and in 1900 only did so in croquet, golf, sailing, and tennis. So if Annie Luker was a diving champion, it wasn't in the Olympics.
I don't see how this can be Hagar, though, as she was born 1870, married in 1890. Although she may have kept her maiden name, she wouldn't have continued to be called 'Miss', I wouldn't think, and the dates for Annie's career suggest a younger woman.
I do see that Hagar's father in 1881 was a swimming master, and that there was a younger sister, listed as Rosa A, b. Tunbridge - maybe she was 'Annie'? Or maybe it was another relative of the family. I note this Luker family are from Abingdon - there's an 1881 census entry for Alfred Luker, 33, b. Abingdon, bath attendant, Amelia, his wife, and children John B, Ann and Rose. In 1901 John B is a theatre attendant and Rose is a music hall artist, I can't spot Ann.