An Eliza Roberts was baptised in Edmonton, 1818, with parents John and Ann. My guess would be the same as it was back in September.
My theory:
Mary Ann Bird bap. Edmonton with parents John and Ann Bird, was your Mary, and married James Mardell in 1830, using her original surname. Although she was brought up using the name Roberts. Father John was a soldier at the time, and was probably the true father of Mary Ann. Down as Bird, instead of Roberts,for the baptism to make the child appear to be legitimate.
It would make sense for her to use the name Roberts on her children's birth certificates. Why announce, in those times, that you were born before your parents married.
Just my thoughts
As a soldier at that time, he may have been unable to stay long enough to arrange a marriage. But when the Napolionic Wars ended in 1815 he was able to settle down.
So John Roberts married Ann Bird in 1816. They then had Eliza in 1818.