Hi Mike,
There are other candidates for your Thomas than the ones already mentioned by Len and Bruce. You need to do some fundamental research before taking this any further back. I do agree that the Thomas and Elizabeth Killip in Whitehaven looks like the most likely couple who emigrated in 1881 although you would need to resolve the discrepancy between Anne E Killip, 9 months in the 1881 census (April 3rd 1881) and the immigration record of Hannah Killip, 9 months in June 1881 - you would need to examine images of the original documents rather than relying on transcriptions. I would also suggest you obtain a copy of Thomas Killip's certificate of marriage to Elizabeth Wilson in June quarter of 1878 in Bootle, Cumberland (Bootle 10b 914 Whitehaven district) as this should confirm parentage and I should be able to help you further at that point. Birth certificates for England can be ordered on-line from the General Record Office(www.gro.gov.uk/gro/content/births/obtainingbirthcertificates/index.asp).
Ian