Just to clarify (as the Ancestry links won't work for everyone) - you are asking if this family in Islington
Thomas Lawrence 32 - bricklayer's labourer
Mary A Lawrence 32
Henry Lawrence 9
Florence Lawrence 5
Jane Lawrence 3
Emily Davey Lawrence 3
RG12, 163, 51, 32
and this in Faversham
Thomas H Lawrence 36 - plumber, painter, glazier b Bridge, kent
Mary A Lawrence 34 - b Preton, Kent
William H Lawrence 12 - b Coperinge, Kent
Frances E Lawrence 10 - b Faversham
Emma D Lawrence 3 - b Faversham
William J Luckhurst 30
RG12, 714, 72, 22
both frmo 1891 are the same. i think not. I can follow the Kent chap through to 1901 and 1911