rossliv - Phebe was a WHITEHOUSE. No known LUCAS connection (even with her siblings, who are well documented). The Patrick/Phebe combination is unusual (especially McD), so I can't help feeling the Wood Street entry is them, but somehow misrecorded. We'll never know.
Thanks for checking.
Hi again,
there are births on Free BMD for Thomas and Margaret McDonald which fit with the ages of the children in 1851.
I have tried to follow them and I think they may be at:
1861 RG9; Piece: 2045; Folio: 64; Page: 5 with a mother Esther

and stepfather Joseph 'Whild'.
1871 RG10; Piece: 2999; Folio: 43; Page: 21
Thomas with wife Sarah and mother 'Eliza Wild'.
1881 RG11; Piece: 2867; Folio: 32; Page: 14
with mother 'Ester While'
Ester's birthplace is Ireland and Derbyshire.
I am bringing them to your attention as possibilities for the 1851 - although there is the discrepancy between Phebe and Ester/Eliza , the children births and subsequent census entry does fit.

This of course would then still leave your Patrick and Phebe as missing.
best wishes
heywood