The only William Whitaker birth I can find in Accrington 1838/1839 is in 1838 - mother's maiden name Pickup.
From the Lancashire OPC site, I got the following:
Baptisms: 19 Aug 1838 St James, Accrington, Lanca
shire, England
William Whitaker - Son of William Whitaker & Betty
Born: 19 Jul
Abode: Grange
Occupation: Printer
Baptised by: J. Hopwood
Marriage: 25 May 1829 St James, Accrington, Lancashire, England
William Whitaker - (X), of Accrington
Betty Pickup - (X), of Accrington
Witness: Titus Welch; James Anderton
Married by Banns by: Jno. Hopwood Minister
Register: Marriages 1829 - 1837, Page 2, Entry 6
If this is the right family, then this would appear to be them in 1851
William Whitaker 42 head, coal dealer
Betty Whitaker 41 wife
Children:
Peter Whitaker 22
Ellen Whitaker 19
John Whitaker 17
James Whitaker 15
William Whitaker 13
Allias Whitaker 11
Thomas Whitaker 8
Haston Whitaker 6
Pickup Whitaker 4
lodger:
John Wilkinson 21
All were born Accrington, apart from Betty who shows herself as born Wissell. I would guess this is likely to be Wiswell (pron Wizzel) which is near Whalley.
There are 2 possibilities for Betty's baptism, but I would favour the second as being nearer to her declared age on the census and also was at Whalley parish chuch.
Baptisms: 4 Dec 1808 St James, Accrington, Lancashire, England
Betty Pickup - Daughter of George Pickup & Betty
Born: 15 Nov 1808
Abode: Accrington
Baptisms: 3 Sep 1809 St Mary and All Saints, Whalley, Lancashire, England
Elizabeth Pickup - Daughter of Ellen Pickup
Abode: Wiswell
Notes: Illegitimate
On the 1861 census, William (snr) shows himself as being 53. there's a baptism in 1807 which may or may not be him.
Baptism: 15 Nov 1807 St James, Accrington, Lancashire, England
William Whitaker - Son of John Whitaker & Alice
Born: 22 Oct 1807
Abode: Accrington
Hope this helps.
ps You're fortunate in that Accrington and Whalley parish churches are old and many of the registers have been transcribed. If you haven't already tried it, have a look at
http://www.lan-opc.org.uk/