Hi Jan,
Here is your family, I think, in 1901:-
1901 Census
16 Service Road, Litherland, Lancashire
William Bennie - Head - md. - 50 - Timber Salesman - b. Scotland
Helen Bennie - w. - md. - 46 - b. Yorks., Holmfirth
Alice Bennie - d. - single - 23 - b. Lancs., Bootle
Catherine Bennie - d. - single - 21 - Teacher School - b. Lancs., Bootle
Helen Bennie - d. - single - 19 - Teacher School - b. Lancs., Bootle
Edith Bennie - d. - single - 15 - Drapery - b. Lancs., Litherland
William Bennie - s. - single - 12 - b. Lancs., Litherland
Rebecca Bennie - d. - single - 8 - b. Lancs., Litherland
Malcolm Bennie - s. - single - 6 - b. Lancs., Litherland
Amelia Bennie - d. - single - 4 - b. Lancs., Litherland
Ref: RG13 / 3449 / ED5 / f.46 / pp. 46 & 47
Litherland is in the north of the city of Liverpool.
The one difference to the names listed on your posting is that William's wife is called Helen - is 'Annie' a nickname for Helen perhaps? William's age fits the bill, though, as does his job.
Is this the correct family?
Regards,
Richard