Are you aware that Reginald Charles John Smart joined the 3rd Hussars with the number 3837 at Aldershot on 23 June 1897, and served there and at Shorncliffe before being discharged at his own request on 25 May 1898? Also I think you have quoted the wrong year of birth for him. It looks like he was born in Pimlico in the last quarter of 1879 (see the 1911 census, plus his birth registration at Hanover Square 1A 399).
I am very confused about his marriage. Clearly in the 1911 census he is living in Newton Abbot with his wife Emily and three sons, including Reginald Albert born 1910. Emily's maiden name was Timms (per Reginald Albert's birth registration), yet it appears that Reginald C J Smart did not marry Emily Timms until Qtr3 1944 (Hendon 3A 1591). The woman he appears to have married in 1900, was either Mary Elizabeth Dennison or Catherine Polly Capewell, in Islington (Qtr 4 1900 Islington 1B 489).
Reginald Charles John Smart's service record for WW1 does not appear to have survived, and I haven't found a WW1 medal card for him, among than many Reginald Smart's who served.
(For the information of anyone else who wants to look into this story, don't be confused by Reginald Charles James Smart born 25 Nov 1901 in Romsey and who married Linda Christian in 1937 (again in Romsey) and who died on 2 Dec 1975 in Romsey)