I just found the marriage for William Tyrer to Catherine McDonald. It seems they did not marry until 1846 at Shoreditch so all children were born out of wedlock. I believe that this may be because William was involved or married to another woman.
I have located a James Gillatt Tyrer born circa 1825 whose father was also William Tyrer Gold beater and wonder if there is a connection. William married a Louisa Richardson in 1812. Louisa was the mother of James.