Hi Miriam - here is all I know.
1. JAMES SULLIVAN (b.c.1797 Cork) and wife ELLEN c.1803, Cork. (Information as to her name & birth from British census 1841-1871 inc.) married in Ireland.
2. They had a daughter HANNAH (possibly more children, but none on 1841 census) in about 1823. UK census returns give Cork and once 'Munster' as place of birth.
3. Between 1823 (Hannah's birth) and 1825, the birth of DENIS the family moved to London. (Denis's place of birth is given as St Andrew's, Middlesex).
4. Sons JAMES (1830), JOHN (1840) and EDWARD (1844) born in St Andrews, Middlesex (the GRO brings up no surname matches for John and Edward and I suspect the children were not registered).
5. DENIS Sullivan (1825-1906, Middlesex) married ELIZABETH CAHLAN (spelling variously Cahalan/Challin/Cahline/Charlan/Charline - these latter 4 on birth registrations. C.1881 Elizabeth states she was" formerly a farmer's wife". This ties in with a comment her grandson made namely that his grandfather had been a farmer in Ireland.
6. Parents of Elizabeth Cahlan were Denis Cahlan c.1786 and Mary c.1803. First sighting of Denis Cahlan (Cahalan) and Mary were in 1851 census, living in same area as their daughter Elizabeth and husband Denis Sullivan.