Probably:

Civil Registration Indexes (Births)
Ethel Wake, reg. 3rd quarter of 1887, Hartlepool, Durham, England.
She was baptised in the Church of the Holy Trinity in Hartlepool, Durham, England on 20 July 1887. Her parents were William and Mary Ellen Wake.

Remark:
Cleveland is a land of hills and dales from the River Tees to Vale of Pickering, England. The name means "cliff-land". Larger towns are Billingham, Guisborough, Hartlepool, and Middlesbrough.

Some more Ethel Mary Wakes:
Ethel Mary Wake, reg. 1st quarter of 1874, Caistor, Lincolnshire, England.
Ethel Mary Wake, reg. 3rd quarter of 1880, Tenterden, Kent, England.
Ethel Wake, reg. 1st quarter of 1883, Brentford, Middlesex, England.
Ethel Wake, reg. 1st quarter of 1885, South Shields, Durham, England.
Ethel Mary Wake, reg. 4th quarter of 1885, Gateshead, Durham, England.
Ethel Wake, reg. 1st quarter of 1889, York, Yorkshire East Riding, England.
Ethel Wake, reg. 2nd quarter of 1890, Darlington, Durham, England.