Hi, I have looked into everything that you all suggested and found that William is definitely Ann's nephew however I have hit two stumbling blocks
Firstly, I cannot find a marriage for Ann at all. I found her on the 1851 census at home with her parents (age 5) then I fund her in 1871 with husband, Thomas Mitchelson. I can find Thomas on the 1871 census living census living with his parents so assuming they got married between 1864 and 1871 but can't find a marriage anywhere

Secondly, Catherine who is Williams mother and assuming she married William Ridley Dixon then went on to marry George Watson - all ages add up etc however I found the probate for William Ridley Dixon with his wife Catherine Dixon living at Shadongate, Carlisle. The same Catherine Dixon is living there in 1871 but with her parents William and Ann Armstrong. It is not the same William Armstrong as the William Armstrong who is the correct Catherines father is living with his wife Mary in 1871 and William Dixon their grandson.
I thought it was all worked out but now I am not too sure