It could be Elizabeth was born in 1837 just before civil registration started.
In 1861 Elizabeth was with her family ay 39 Ernest Street, St Pancras. Her father was George Frod, bootmaker, born 1811 Spitalfields; her mother was also Elizabeth, born 1806 Gloucestershire. There were two brothers Henry George, born 1835 St Pancras; and Frederick, born 1845 St Pancras. The family were at the same address in 1851.
In 1841 they were at George Street, St Pancras.
Interesting that Elizabeth senior was born in Gloucestershire, so was George Brinkworth, is there a connection?
I'll have a quick look for Elizabeth's baptism and George/Elizabeth's marriage.