Emma Raducanu won on her Centre Court debut beating Belgium's Alison van Uytvanck, while Murray recovered from losing the opening set to progress past James Duckworth.
British number one Cam Norrie and defending champion Novak Djokovic also got through.
Two of the all-time greats begin their campaigns later.
Serena Williams makes her return to singles action after a year out against Harmony Tan.
While 22-time Grand Slam champion Rafa Nadal faces Francisco Cerundolo.
Women's world number one Iga Swiatek has the honour of playing first on Centre Court.