The following children (at least) are listed on the IGI. (Some of them were listed previously for us). They have the right names to be connected with our family, but. . .
John Christened Ormskirk 11/10/1802
Thomas Christened Ormskirk 14/3/1806 (c.f. our Thomas born c. 1801)
Sarah Christened Ormskirk 22/11/1809
Charles Christened Ormskirk 04/9/1812
Ralph Christened Ormskirk 29/9/1816
Edward Christened Ormskirk 20/9/1818
The Charles Balshaw in Altrincham was born in Ormskirk. From various soruces his date of birth was as follows:
A Ralph Balshaw died in Ormskirk in 1839 (according to civil registration) but it is not clear whether he was this one.
Conclusion. These were not Thomas' parents and siblings.
From the IGI for Lancashire - John Balshaw married Nancy Cocking, at Liverpool St Nicholas, on 19 September 1792. It is not clear whether these are the same people.
From Pevsner - Our Lady and St Nicholas, Liverpool, known as St Nicholas. The oldest part of the church is now the steeple, built 1811 to 1815. The church was destroyed during WW2 and the replacement was completed in 1952.
A John and Nancy Balshaw (possibly the same people) lived in Ormskirk soon
after this and had the following children:
Thomas, Christened 9 August 1801 (c.f. our Thomas who was born in 1801)
Margaret, Christened 18 March 1804
Ralph, Christened 2 October 1811
Elizabeth, Christened 23 October 1816 (only Nancy's name is given)
Perhaps this John was a brother of Ralph, and perhaps therefore Thomas and Charles (of Altrincham) were cousins. Holdens Annual London and Country Directory of the United Kingdom and Wales in three volumes for the year 1811 gives three entries who may have been John and his brothers (Ralph and Chas), all cabinet makers, all in Church St. Note that my great great great grandfather Thomas left his joiners tools to his son Henry in his will, suggesting further evidence of a connection.