Hi ronneynel,
You may already have this from the 1841 census. I thought the family names were interesting considering the names that Edward gave his children, and something to keep in mind if you can prove his connection to Manchester.
1841
Shude Hill, Salford
Manchester
CUNINGHAM
Peter, 45, clothes dealer, born Ireland
Anne, 40, born Ireland
Catherine, 17, cap maker, not born in county
Mary, 15, cap maker, not born in county
Ellen, 13, not born in county
Hugh, 11, not born in county
Edward, 9, not born in countyPeter, 6, born in county
John, 3, born in county
Sarah, 15 months, born in county
The first four children, including Edward, were possibly also born in Ireland, or even Scotland. I am struggling to find entries for any of these people in 1851 - anything can happen in 10 years!
Available immigration records are nowhere near complete, and he may just be one of those who is not recorded. Have you had a look at the Edward CUNNINGHAM who arrived on the
Joseph Soames in 1847? He was tried at the Old Bailey on 5 Jan 1846 and sentenced to 10 years. http://www.oldbaileyonline.org/browse.jsp?id=def2-380-18460105&div=t18460105-380 He wasn't necessarily from London - his partner in crime, William BREESON, was from Lynn in Norfolk. Edward was aged 16 on the ship's muster, and his usual occupation is given as Tailor, so he may have been serving an apprenticeship.
The
Joseph Soames arrived with exiles at Port Henry (Geelong) via Tasmania in Sep 1847, and "....those bearing good characters are ordered to be discharged on their arrival in the colony on condition of remaining as settlers for life."
Edward CUNNINGHAM is noted as being amongst those "sent on shore not having obtained employment to their liking onboard."

An excellent and quite funny article by a Mr Broadway who was the second mate on the 1847 voyage:
http://trove.nla.gov.au/ndp/del/article/4768906?searchTerm=%22joseph%20soames%22Others relating to the arrival of the
Joseph Soameshttp://trove.nla.gov.au/ndp/del/article/12892725?searchTerm=%22joseph%20soames%22http://trove.nla.gov.au/ndp/del/article/2970724?searchTerm=%22joseph%20soames%22http://trove.nla.gov.au/ndp/del/article/8761384?searchTerm=%22joseph%20soames%22I can't see a marriage for Edward and Elizabeth either. Do you know anything at all about her - where she came from, parents' names?
Debra