Possibly Wrexham was the registrationcentr for Birkenhead.
The only Cheshire-born Margaret Roberts with the right age (age 4 in 1861), in the Free BMD birth index, is in the Apr-May-Jun quarter of 1856 in Wrexham volume 11b page 342.
a birth certifiate (7 pounds or so from the GRO) would give the mother's maiden name.
Similarly Martha (age 8 in 1871)is in the Apr-May-Jun quarter of 1862 vol 11b page 370.