Other tour stops will include Darlington, Cambridge, Richmond, Malvern, Swansea, Truro, Northampton, Coventry, Bromley, and Brighton.
The show, which played a limited season at the Arts Theatre last spring, explores relationship between the two screen legends during their time filming Whatever happened to Baby Jane?.
Dobson's stage credits include Calendar Girls, Hello, Dolly!, and Thoroughly Modern Millie. She may be best known for her portrayal of Angie Watts on the television series EastEnders.
Among Scacchi's recent stage credits are A Little Night Music, Private Lives, and Deep Blue Sea. She is currently appearing in David Williamson's new play Nothing Personal in Sydney, Australia.