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Britain's Got Talent judge Amanda Holden, TV presenter Myleene Klass and Coronation Street's Charlie Condou were among the well-wishers on Twitter.
Although not officially confirmed by the star's publicist, Allen tweeted last night: "Totes Amaze."
Corrie's Condou verified the birth reports to his followers, tweeting: "She has indeed, a little girl," while Culture Club singer Boy George wrote, "Congrats to Lily Allen on her sprog".
Holden said: "Massive congrats to Lily and [husband Sam Cooper]! Such good news. Xxxx," while Klass simply used the social networking site to say, "Congrats".
Ex-boyfriend Seb Chew broke the news yesterday evening, writing: "Sending out love to lily, sam and mini cooper...... YES."
Cooper announced Allen's pregnancy during their wedding reception back in June. The couple lost a baby in November 2010, six months into Allen's pregnancy.
