Hi,
Here's your Henry on 1841, if you use ancestry he is transcribed as Fennick:
Newgate Street, Morpeth (H0107/835/12, Page 2, Folio 34)
William Fenwick, 45, Shoem (all born in county)
Isabella " , 45
James " , 20 Shoem
William " , 15
Isabella " , 14
Henry " , 12
Rachel " , 8
Solomon " , 6
Looking at where he is in the order of the siblings, probably not born 'out of wedlock', but I suppose there is still the possibility that his mum was married before and William is her second husband. I'll dig around some more.
Kath