James's father Lace Radcliffe wrote in 1877 that James was now in Australia.

It is much easier to trace back from a known event than forwards, so if James was your ancestor do you have any Australian records which put him in a particular place with a date? Marriage and/or death certs?

Can you be certain this isn't him in the 1851 IOM census:
Ancestry index:
Name:
Jas Radcliffe
Age: 18
Estimated Birth Year: abt 1833
Where born:Andreas, Isle of Man, Isle of Man
Relation:Assistant
Gender:Male
Civil Parish or Township: Maughold
Town:Ramsey
County/Island:Isle of Man
ED, institution, or vessel:1b
Household Schedule Number:57
Piece:2524
Folio:315
Page Number:15

Household Members:
Name Age
Robt Craine 23
Jas Radcliffe 18

Robt Craine was a Grocer Wine & Spirits Dealer b. Ballaugh; Jas Radcliffe Assistant Grocer b.Andreas.

Sue