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why does that cut down the search?

As all the children were born in England and the first known child was born in 1904 then that means that the couple arrived in Britain before this date so that cuts your search for their entry into the country down to before 1904.

For info:-

England & Wales, Marriage Index: 1916-2005 about Restituda Ferri
Name: Restituda Ferri
Spouse Surname: Jordan
Date of Registration: Jul-Aug-Sep 1931
Registration district: Liverpool
Inferred County: Lancashire
Volume Number: 8b
Page Number: 351
Find Spouse: James F Jordan
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Will pm possible children to this marriage. Maybe you could try and contact a member of the family who may have more information to help you in your research.
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England & Wales, Death Index: 1916-2006 about Restituda Jordan
Name: Restituda Jordan
Birth Date: 22 Sep 1912
Date of Registration: Jan 2000
Age at Death: 87
Registration district: Liverpool
Inferred County: Lancashire
Register Number: G26D
District and Subdistrict: 0251G
Entry number: 71

Just wondering who Nunzio Vano was and found this:-

England & Wales, Marriage Index: 1916-2005 about Nunzio Vano
Name: Nunzio Vano
Spouse Surname: Wyatt
Date of Registration: Oct-Nov-Dec 1920
Registration district: Newton Abbot
Inferred County: Devonshire
Volume Number: 5b
Page Number: 338
Find Spouse: (don't know why, but can't see name of spouse?)

from ancestry:-
Marriages Dec 1920 (>99%)
Vano Nunzio Wyatt Newton A. 5b 338
Wyatt Florence V Vane Newton A. 5b 338
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Possible children for this couple:-
Births Dec 1921 (>99%)
Vano Norman V Wyatt Newton A. 5b 193
Births Mar 1930 (>99%)
Vano Beryl J Wyatt W.Derby 8b 617
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Looks like he may have ended up in Australia:-

Nunzia Vaiano
Australian Electoral Rolls, 1903-1980
Nunzia Vaiano
Australian Electoral Rolls, 1903-1980
Nunzia Vaiano
Australian Electoral Rolls, 1903-1980