2005 is an old post to reply to but in case you are still looking ....
There is a slim chance that your William Anderton/Egerton may be the following: (lancs parish clerks) Baptisms: 5 Oct 1806 St Mary the Virgin, Prescot, William Anderton - Son of William Anderton, late & Mary Born: 21 Sep 1806Abode: PrescotOccupation: Collier
William Anderton senior died in a pit fire in 1805 in Whiston.His wife may have died in 1810: (lancs parish clerks) Burial: 15 Apr 1810 St Mary the Virgn, Prescot, Lancashire, England Mary Anderton, Widow -Abode: Prescot
William would have been orphaned at 4 years old and would have presumably have been brought up by relatives.That may possibly account for a change of surname?But perhaps your theatre connection makes a stage name seem more probable?
I can't find a brother George for this William. Best wishes.