According to FindMyPast Egerton was baptised at St. Mary, Uttoxeter (but married at Hanbury by licence).
The only likely couple I can see for his parents are Joseph Adams and Elizabeth Painter, both of Marchington, who married by licence 4/2/1718 Hamstell Ridwell. A daughter Dorothy bp.3/4/1720 Marchington and then I think they moved around with a Joseph bp.3/12/1721 Checkley, Mary bp.29/3/1725 Darlaston and Hannah bp.14/8.1827 Darlaston followed by Egerton.
There was another Joseph and Elizabeth baptizing children in Burslem but they were baptising children before 1718.
Annette