Any Cowen Cowan, Cowing have any possible ancestors to Thomas Cowen? This is my paternal line and I'm so stuck and feeling desperate to find something!

Thomas Cowen born around 1855-1860 born Hexham
married Rachel Lewis in Carlisle 1876
Children Margaret (Maggie)1879 all born in Carlisle
Annie 1884
John James (known as James) 1885/1916
Mary J 1891-1893
Thomas William 1898-1901

I wonder if there is anyone else researching these people, I'm constantly trying to find Thomas Cowen's birth details as he states in 1881 & 1891 he was born in Hexham, Northumberland then 1901 that he was born in Carlisle.

I've been searching both areas, bought certificates and found nothing to connect so far.
His marriage certificate says his fathers name was William and occupation a Carter that didn't help either as I couldn't find him and I was advised that not all fathers mentioned on the birth certificate are actually their fathers names, to hide illegetimacy etc.