freeBMD lists 171 people named Wincup but only a few in Lancashire. Their list with GRO reference numbers is below - they seemed to be good at death, not much on birth:
Name Year Quarter Record Type District County
Wincup, Ann 1886 March Deaths Chorlton Lancashire
WINCUP, Jane 1843 June Deaths Ashton under Lyne Cheshire Lancashire
WINCUP, Mary 1838 June Deaths Manchester (1837-1924) Lancashire
WINCUP, Mary 1851 March Deaths Manchester (1837-1924) Lancashire
WINCUP, Sarah 1873 March Deaths Manchester (1837-1924) Lancashire
Wincup, William Henry 1902 June Marriages Liverpool (1837-1924) Lancashire
There are Wincups elsewhere but the most significant for your search for James might be:
WINCUP, Herbert James 1871 September Births Blything Suffolk
Wincup, James 1871 June Marriages Blything Suffolk
Wincup, James 1874 March Births Holbeck West Riding of Yorkshire
WINCUP, James 1874 March Deaths Holbeck West Riding of Yorkshire
WINCUP, James 1877 June Deaths St Olave Southwark London Surrey
Wincup, James Horace 1901 March Births Hartlepool (1859-1938) Co. Durham
WINCUP, James William 1860 September Births Wangford Suffolk