Well, didn't quite need the white gloves this time -
no William Wilcock in Halton I'm afraid, but I did find a very promising John Wilcock.
From LPRS vol 126:
Baptism 15 July 1832
JANE d. William and Ann of Force Bank, Halton, labourer
Baptism 6 July 1834
JOHN s. William and Ann, Force Bank, Halton, labourer
Force Bank is by the River Lune up river from the main Halton village, you can see it on the Old Maps site. So maybe 'Orton' is indeed Halton

Other Wilcocks in the Halton vol 126 (it started raining! so I stayed put):
Baptism - 13 March 1808 Thomas s. James and Sarah Wilcock, Intack House, Halton born 22 Feb 1808 (not in BTs)
Marriage - 18 May 1782, Robert Wilcock of Nether Kellett, husbandman and Mary Crosdale of Halton
Marriage - 16 May 1807, James Wilcock, husbandman of Bolton le Sands & Sarah Howson, spinster of Halton
Burials
15 Feb 1808 Grace wife of Richard Wilcock, Halton
22 Jan 1828, Richard Wilcock age 88.
The name Wilcock occurred several times in the books for Ingleton and Warton, but they only went up to 1812. There was also a marriage in Tatham Church
2 June 1827, Edward Wilcock of Melling, collier & Mary Birkett of Tatham. but no other Wilcocks in Tatham.

Barbara