Birth: April 1891 Southampton, Hampshire, UK
Father: George Croucher 1863-1924
Mother: Alice Maud M Oakley c1865-1924
Death: January-March 1895 Southampton, Hampshire, UK
I suspect that the relevant entry in FreeBMD is for the birth of Arthur Edwin Crouch in April-June 1891 in Southampton (2c 5).
In the 1891 census as Arthur Croucher aged 1, born in Southampton, Hampshire, and living with his parents (George and Alice), brother (William), and two sisters (Alice and Ethel) at 122 Northumberland Road, St Mary, Southampton, Sussex. His widowed grandmother and aunt were living at the same address.
I also suspect his death is in FreeBMD as Arthur Edwin Y Crouch in January-March 1895 aged 3 in Southampston (2c 3).
Matt Sheppard and Philip McCauley have entries in Ancestry Public Member Trees for Arthur Croucher born in about 1890 in Southampton, parents George Croucher and Alice Maud Oakley.