Liverpool Bewley's

Looking for info on Liverpool Bewley's connected to the Dublin Bewley's My Gr grandfather George Henry Bewley was a coffee miller he also had flour mills he lived in Liverpool in the late 1800's He was born in Dublin not sure of date i would guess 1850's as my grandfather was born 1883 and had an older brother also believed to be a George. Unfortunately this is about the only info i have, as the info has been passed down and my grandfather died long before i was born so all i have is a few story's and a couple of documents to go on. I do know they are related somehow to the Bewley's of Dublin as my grandfather said he was, he also took my grandmother from Belfast to Dublin to the coffee shop and he was warmly greeted and well known by them.
Note I did find a family in Liverpool on the UK census but it turns out not to be the correct one as he as the same wife in all the census searches and George Henry married twice due to the death of his first wife His second marrige was around 1888-8889 i believe because from what has been passed down my grandfather went to live with his grand mother when he was five due to the step mother and him not getting along.
I thank you for any help that you can give.
Karl Bewley