There were several Daly's in the 1871 Census but none that fit your family.The only Bridget was spelt Dayley and she was 28 Cotton Card Room Hand and was a boarder at Bamfield Lodging House in Stockport. So the family just of come over just after that. I have the 1871 Census that only identifies those born in Ireland.
There are 185 JOHN Daly's in Cork in 1853, for the Griffith Valuation with all occupiers of land listed. www.askaboutireland.ie
Just too many to even make a start. If you had Elizabeth's maiden name from Bridget's birth record I could cross reference the Parish's as this is probably where the family that stayed behind lived.
Denis Daly there are 4 in the 1911 Census for Cork 224 in All Ireland.In 1911 there are 109 Daniel Daly's in Cork.
No Denis Daly in the UK 1901 Census. I looked through just one list of 1980-1960 Passenger ships records 11 Daniel and 3 Dennis mostly to USA.
The current online telephone directory shows 642 Daly's in the County of Cork. Quite a few named Denis, several D's but no Daniel's. Families did follow christian names through generations, I would mail letters to a few of the Denis Daly's. You can also run an ad or letter to the editor
about your search while you wait for connections over the internet.
There is a bmd Foundation website online but for only 1/2 of Cork, the North East portion. There are 2 Bridget Daly's born in 1854, and just one with a father John. This is a not-for-profit website but a fee is charged. If this is the correct family, you will get the date, where/parish and mother's maiden name. You need to contact me for the website
as it is not a free one.