Have you checked freebmd for his other marriages? 1929 to Florence Rampton is a possibility if his father was Henry Joseph Alexander
His birth reg is on freebmd but you have his full birthdate from his death reg
james arthur alexander was on 11th of march 1908 i think he was born in hendonSep 1889 Pancras 1b 267
BRADSELL John Henry C
MARMOY Amelia Elizabeth
BRADSELL, JOHN EBENEZER mmn MARMOY
died 1890
GRO Reference: 1890 M Quarter in PANCRAS Volume 01B Page 27
BRADSELL, JAMES HENRY mmn MARMOY
died 1892
GRO Reference: 1891 D Quarter in PANCRAS Volume 01B Page 69
Mar 1935 Willesden 3a 524
ALEXANDER Henry J
MARMOY Amelia E
1911:
https://www.familysearch.org/ark:/61903/1:1:XW43-D4DALEXANDER, JOHN THOMAS mmn MARMOY
GRO Reference: 1893 J Quarter in PANCRAS Volume 01B Page 4
ALEXANDER, HENRY JOSEPH mmn MARMOY
GRO Reference: 1895 M Quarter in MARYLEBONE Volume 01A Page 608
ALEXANDER, ARTHUR GEORGE mmn MARMOY
GRO Reference: 1895 J Quarter in MARYLEBONE Volume 01A Page 597
1901:
https://www.familysearch.org/ark:/61903/1:1:X9C5-R6RALEXANDER, ALFRED EDWARD mmn MARMOY
GRO Reference: 1897 M Quarter in HENDON Volume 03A Page 205
ALEXANDER, WILLIAM GEORGE mmn MARMOY
GRO Reference: 1899 M Quarter in HENDON Volume 03A Page 265
ALEXANDER, ADA AMELIA mmn MARMOY
GRO Reference: 1900 S Quarter in CAMBERWELL Volume 01D Page 857
ALEXANDER, AMELIA ROSINA mmn MARMOY
GRO Reference: 1901 S Quarter in HENDON Volume 03A Page 270
Married:
Jun 1923 Willesden 3a 507
HINGSTON George W F
ALEXANDER Amelia R
ALEXANDER, LILY ELIZABETH mmn MARMOY
GRO Reference: 1903 D Quarter in HENDON Volume 03A Page 249
Married:
Jun 1924 Willesden 3a 530
ADAMS John A
ALEXANDER Lily E
ALEXANDER, FRANCIS JAMES mmn MARMOY
GRO Reference: 1906 M Quarter in HENDON Volume 03A Page 327
ALEXANDER, JAMES ARTHUR mmn MARMOY
GRO Reference: 1908 J Quarter in HENDON Volume 03A Page 321
ALEXANDER, CHARLES STANLEY mmn MARMOY
GRO Reference: 1910 J Quarter in WILLESDEN Volume 03A Page 327
ALEXANDER, ADA MAY mmn MARMOY
GRO Reference: 1912 J Quarter in WILLESDEN Volume 03A Page 547
Married:
Sep 1933 Willesden 3a 1116
BLACK Alfred
ALEXANDER Ada M
ALEXANDER, IVY GRACE mmn MARMOY
GRO Reference: 1915 D Quarter in WILLESDEN Volume 03A Page 528
Married:
Mar 1938 Willesden 3a 588
BLACK Albert
ALEXANDER Ivy G
Jamjar