I was randomly researcing Edwin Moseley when I came across your enquiry. I am not sure how much you know about the family but I will tell you what I know.
Edwin was my great great grandfather. He was born in Clerkenwell,London on the 31 March 1812 and had a younger brother Francis Andrew, born 30.10.1814. He was baptised at the Lady Huntingdon's Chapel, Clerkenwell on 25.10.1812.
His father was Francis Moseley and his mother Louisa. I believe that Francis was a surgeon who lived at 38 Houndsditch.
I was always told that the family descended from Sir Nicholas Moseley, who was Lord Mayor of London in the 1590s and who subsequently dropped the second e in his name. I once saw a family tree which purports to show this link, but I am unsure where it is. I have a cousin who has a portrait of Sir Nicholas. That side of the family were Lords of the Manor of Manchester and their descendents include Sir Oswald Mosley, the well known fascist.
Our side came, I believe, from Buildwas in Shropshire, but I have no real proof of that.
As you rightly say Edwin married Mary Doyle. Her brother, Sir William, went on to become Chief Justice of Gibralter ( 1877 to 1879 ) where a portait of him hangs in the Supreme Court, having been knighted at Windsor Castle on 12.12.1873. He died in Cheltenham on 27.4.1879. His family home,Villa Doyle, now houses the National Art Gallery in Nassau.
Edwin had 8 children, of which I am ashamed to admit I only know the names of the boys: Henry Edward, died 1884; Alfre Edwin, died 1904, Francis Arnold, died 1919; William, died 1884; Charles Herbert Harley1857 to 1933; and Percy James,died 1887.
One of the sons went on to become a Judge in Australia.
My great grandfather was Charles Herbert Harley Moseley, who became Governor of Lagos ( as Nigeria was then known ) from about 1901 to 1904.He died in 1933. He had 2 sons, Oswald Herbert George Kerr and Reginald Anthony Dean.
Oswald, my Grandfather, was a director of Hawkins and Tipsons, Ropemakers and his brother was a Brigadier in the British Army.
Oswald had 4 children, of whom my mother Diana was the younger daughter. Her elder sister and brother died in the last war, leaving her and her brother, Peter, who lives in Ireland. He has a son and 2 daughters and 2 Moseley grandsons, so the name lives on in Ireland.
All the above information was collated by my father and, in time, I would like to research the Moseleys and the Doyles further back. Should you have any further info I would be very interested. Equally I have only given you some of what I know for fear of boring you to death! The cousin I referred to has more.
With best wishes
PS What is your interest ?