Has any member of the British royal family ever committed suicide ?

Prince Alfred of Edinburgh, a grandson of Queen Victoria. The exact circumstances of his death in 1899 are unknown. It is now generally accepted that he shot himself, but at the time his death was variously reported as due to TB or a tumour. What is known is that he caught syphilis during his service as a Guards officer and, left untreated, this can lead to mental difficulties. He did not attend his parents' Silver Wedding celebrations on January 22nd 1899, the reason being given as nervous depression. He shot himself while the rest of the family were at the celebration and later died on February 6th. 1899.

https://en.wikipedia.org/wiki/Alfred,_Hereditary_Prince_of_Saxe-Coburg_and_Gotha