I may have a connection with your Birchall family. I have a Jane Birchall who married Edward Parry <1808. They lived in Liverpool on Gradwell and Roscoe Streets between 1811 and 1818.There childrens' names were William (bapt.May 13,1808), Mary Ellen(born Feb.06,1811 and bapt.March 25,1811),Elizabeth(bapt.Dec.10,1815),and Ann Jane(bapt.Aug.23,1818). They were all baptized in St Peter's Church in Liverpool. As you will see many of the same names have been repeated and during that time frame they tended to follow a certain pattern for naming offspring. So there is a possiblity that your Birchalls and mine are somehow related.Please get back to me with your impressions.