Haverfordwest is the county town of Pembrokeshire, Wales
As she was born in 1918 a quick search of 1901 Census, 1910 Census and Pembrokeshire church records between 1900-1912 on familysearch.og found the following 7 Beckett's, which may (or may not) be her ancestors
Florence Mary Beckett
Wales, Pembrokeshire, Parish Registers, 1538-1912
baptism: 25 May 1902
Maenclochog, Pembrokeshire, Wales
Mary Ellen Alexandra Beckett
Wales, Pembrokeshire, Parish Registers, 1538-1912
birth: 31 May 1911
baptism: 19 June 1911
Milford Haven, Pembrokeshire, Wales
William M Beckett
Son
England and Wales Census, 1901
birth: 1900
Maenclochog, Pembrokeshire
residence: 31 March 1901
Maenclochog, Pembrokeshire, Wales, United Kingdom
father: Charles Beckett
mother: Mary A Beckett
Dorothy Mary Beckett
Daughter
England and Wales Census, 1911
birth: 1908
Pembroke Saundersfoot, Pembrokeshire
residence: 1911
St Issells, Pembrokeshire, Wales, United Kingdom
father: Albert Beckett
mother: Mary Beckett
Albert Beckett
Son
England and Wales Census, 1911
birth: 1905
Pembroke Saundersfoot, Pembrokeshire
residence: 1911
St Issells, Pembrokeshire, Wales, United Kingdom
father: Albert Beckett
mother: Mary Beckett
other: Thomas Tresseder, Thelma Beckett, Dorothy Mary Beckett, Mary Beckett
Thelma Beckett
Daughter
England and Wales Census, 1911
birth: 1910
Pembroke Saundersfoot, Pembrokeshire
residence: 1911
St Issells, Pembrokeshire, Wales, United Kingdom
father: Albert Beckett
mother: Mary Beckett
other: Thomas Tresseder, Albert Beckett, Dorothy Mary Beckett, Mary Beckett
Arthur Edwin Beckett
Wales, Pembrokeshire, Parish Registers, 1538-1912
marriage: 12 October 1918
marriage banns: Pembroke Dock, St John, Pembrokeshire, Wales
spouse: Edith Kate Lodge