I don't have access to the 1871 census, but could they have married later than you thought if you didn't find the couple in 1881?

There were two Annie/Anna Corletts around the right age, born Ramsey, in the 1881 census:

Thomas KERMODE Head M Male 69 Maughold, Isle of Man, England Farmer of 20 Acres
Jane KERMODE Wife M Female 67 KK Bride, Isle of Man, England
Eleanor KELLY Niece U Female 22 Andreas, Isle of Man, England General Servant
Annie CORLETT Boarder U Female 21 Ramsey, Isle of Man, England Schoolmistress
Source Information:
Dwelling Ballajora
Census Place Maughold, Isle of Man, Isle of Man
Family History Library Film 1342345
Public Records Office Reference RG11
Piece / Folio 5600 / 20
Page Number 12

John O. QUILLIAM Head M Male 28 Liverpool, Lancashire, England Boot Manufacturer
Myra QUILLIAM Wife M Female 24 W Wycombe, Buckingham, England
John V. QUILLIAM Son Male 2 Liverpool, Lancashire, England
Frederick S. QUILLIAM Son Male 8 m Liverpool, Lancashire, England
Nelly BROWN Serv U Female 16 Liverpool, Lancashire, England General Servant (Domestic)
Anna CORLETT Serv U Female 23 Ramsey, Isle of Man, England Boot Shop Assistant
Source Information:
Dwelling 107 Park Lane
Census Place Liverpool, Lancashire, England
Family History Library Film 1341866
Public Records Office Reference RG11
Piece / Folio 3615 / 95
Page Number 21

This last one Anna/Hanna seems likely?

Sue