There's just a chance that the children could have been registered in Romford and West Ham districts as Barber.
With mother's maiden name Baker (see Mabel's post)
Emma Elizabeth, March 1888, Romford
Frederick William, March 1890, Romford
Adeline, Sep 1892, West Ham
George Thomas, June 1895, West Ham
Frances Ada, Dec 1897, West Ham
Caroline Barbara, March 1901, West Ham
Might be them in 1891, no George Smith, was Emma then enumerated in two different places? Or it could all be wrong!
https://www.familysearch.org/ark:/61903/1:1:QGVN-Q3ZPossible Barber-Baker marriage in Gravesend in 1887. Don't know if it might be on CityArk (won't work for me at the moment)
1911 free index, Barber.
https://www.familysearch.org/ark:/61903/1:1:XWF3-D3G