Thank you for all your responses!
I got the following from the 1881 census
Edward BAWDEN Male 48 Marown, Isle of Man, England
Eleanor M. BAWDEN Female 38 Patrick, Isle of Man, England
Fanny E. BAWDEN Female 19 Marown, Isle of Man, England
Fredk. W. C. BAWDEN Male 13 Marown, Isle of Man, England
Thomas BAWDEN Male 11 Patrick, Isle of Man, England Scholar
Arthur J. B. BAWDEN Male 9 Patrick, Isle of Man, England Scholar
Isabella K. BAWDEN Female 7 Patrick, Isle of Man, England Scholar

I believe that Fanny and William had at least one son, Dr Kit Cole but have been unable to find a record of him and the family say they went to Africa for mining.