My Robert Brogden is happily living in Birkenhead by the 1851 census; and was already in Liverpool by 1841
June, have looked at Yorkshire possibilities including the Downham/Whalley area, following censuses forward, there is a Robert Brogden who seems to fit for Downham in Burnley for 1861. Also looked at Bilton near Wetherby, but census data seems to suggest again any possible Robert stayed within that area.
Don't know if I am clutching at straws but just found that there was an area in Salford called Little Bolton, don't know whether that could be the Bolton link that would fit with Marshall being his father. Of course Marshall seems to have moved around quite a bit so it could be he resided in Bolton for a period, as there is a gap between the birth of Robert around 1811 and the next child Maria, christened in Ardwick in 1816