Yes Eric, the English language version by Cilla is the original.
Although the original Italian version by composer Umberto Bindi was not a hit, even in Italy, the song came to the attention of UK record producer George Martin, who commissioned an English version to be recorded by his protégée Cilla Black. The English lyrics were written by Carl Sigman whose son Michael Sigman would recall: "Inspired by Umberto Bindi's haunting melody, Carl evoked Gino Paoli's Italian title ('Il Mio Mondo' or 'My World'). But he created a wholly original English lyric."[1]
Black cut the song "You're My World" — as Carl Sigman entitled his English language rendering of "Il Mio Mondo" - in a session at Abbey Road Studios with Johnny Pearson conducting his orchestra on 3 April 1964[2] and The Breakaways providing background vocals. Black has said that her road manager and future husband Bobby Willis also sang on the track. Judd Proctor was the lead guitarist on the session[3] which also featured drummer Kenny Clare.[2]
"You're My World" reached No. 1 in Britain on the chart dated 30 May 1964 and remained there for a total of four weeks, one week more than Black's preceding single "Anyone Who Had a Heart".[4] Although Black returned to the UK Top Ten eight times, the song was her final No. 1 hit.