Hello again,
The reason that I believe this to be an estate cottage is that I once knew someone who worked for the Delves Broughton family on their estate at Doddington Hall. This would have been a bit later than the 1920s, she died in 2004, aged 89. She lived in an estate cottage in Walgherton when she worked for them.
The Cheshire Tithe maps which are online, suggest that the Delves Broughton family owned Walgherton lands.
Jo.