As far as I am aware, the first three children were all registered as BENOIT, it was only after the name change, as you have indicated, that the final two children were registered from birth as NUTKINS. The children were:
Henry Louis BENOIT (1902-1903)
Harold John BENOIT (1904-1988)
Gladys Maude BENOIT (1908-1951)
Children born after the name-change in 1909 were given the name NUTKINS from birth, namely:
Elsie Blanche NUTKINS (1910-1943)
Stanley Frederick NUTKINS (1912-1992)
Not sure if you have this info. so posting just in case......
9 Mar 1902 St Mary Bryanston Sq Westminster
Henry Louis Benoit born 18 January 1902
Parents
Louis, glass cutter &
Maud Catherineabode 76 Seymour Place
7th Dec 1904 St Marylebone St Matthew, Westminster
Harold John Benoit, born 24th Oct 1904
parents
Harry Lewis, glass cutter &
Maud Catherineabode 44 Linhope St
17 May 1908 St Matthew, St Marylebone Westminster
Gladys Maude Benoit born 3rd April
parents
Louis, caretaker &
Maude Catharinaabode 44 Linhope Street
surname transcribed as Nuttings
4th Sept 1910 St Matthew, St Marylebone
Elsie Blanche Nutkins born 6 Aug 1910
Parents
Harry, school keeper &
Catherine Maudeabode 44 Linhope St Dorcet Sq
didn't spot a baptism for Stanley Frederick Nutkins