Here are the names I think are possibly/probably those I can identify on CWGC. Have also tried to match to possible 1901 census entries.
Perhaps there will be a pattern in the addresses and areas which will throw up some more clues
John Bernard & Henry Thomas Eighteen
Son of Mr. and Mrs. F. S. Eighteen, of Reading, Berks.
(Brother of Henry Thomas Eighteen - see 1901 Census RG13/1152/45/6)
Civil Parish: St Giles
Ecclesiastical parish: St Bartholomew
CHARLES EDWIN BOSTWICK
Son of Mr. C. H. and Mrs. L. Bostwick, of 64, Amity Rd., Reading, Berks.
FRANIS SYDNEY BRAIN
Son of Sydney and Gertrude Mary Brain, of "Kelvin," 48, Alexandra Rd., Reading. B.A. (Cambridge). Scholar of Trinity Hall, Cambridge.
(1901 census RG13/1150/1256
Civil Parish: St Giles
Ecclesiastical parish: St Giles and St Luke
WILFRID WALLACE DRAKE
Son of Mr. and Mrs. William Drake, late of Stalham, Norfolk; husband of Gladys Drake, of Reading, Berks.
http://www.cwgc.org/search/casualty_details.aspx?casualty=1399471901 in Norfolk RG13/1821/12/15
POSSIBLY..
ARTHUR E FREEMAN
513651 London Regiment (London Scottish)
Son of James and Mary Elizabeth Freeman, of 8, Castle St., Reading.
http://www.cwgc.org/search/casualty_details.aspx?casualty=6468901901 CENSUS RG13/Piece/1144/113/30
Civil Parish: St Mary
Ecclesiastical parish: St Mary the Virgin
POSSIBLY...
HORACE HARDING
Can't identify on CWGC
1901 CENSUS RG13/1152/50/15
Civil Parish: St Giles
Ecclesiastical parish: St Bartholomew
WALFORD VERNON KNOWLES
Son of Vernon and Winifred Knowles, of 7, Bloomfield Avenue, Bath. Born at Reading.
http://www.cwgc.org/search/casualty_details.aspx?casualty=4917411901 CENSUS RG13/1148/11/13
Civil Parish: St Giles
Ecclesiastical parish: St Giles and St Luke
STANLEY H MAY 137850 ROYAL ENGINEERS
Son of John Herbert May, of "Shalbourne", Shinfield Rd., Reading. Native of Beckenham, Kent.
http://www.cwgc.org/search/casualty_details.aspx?casualty=4870901901 CENSUS RG13/1145/30/18
Civil Parish: St Mary
Ecclesiastical parish: Holy Trinity
CHARLES WILLIAM MOSS Royal Berkshire Regiment
Son of Charles and Margaret Moss, of Reading; husband of Edith Clara Moss, of "Dunnville," 118, Basingstoke Rd., Reading.
http://www.cwgc.org/search/casualty_details.aspx?casualty=1858341901 CENSUS RG13/1150/144/4
Civil Parish: St Giles
Ecclesiastical parish: St Giles and St Luke
HORACE L PINKER 203760
Son of John and Jane Pinker, of Reading.
http://www.cwgc.org/search/casualty_details.aspx?casualty=3377391901 CENSUS RG13/1148/24/39
Civil Parish: St Giles
Ecclesiastical parish: St Giles and St Luke
JOHN SATCHELL
Royal Marine Light Infantry Submarine Mining Block "C" PO/3333 (S)
Son of John and Ella Satchell, of "Highclere," 54, Westbrook Avenue, Margate. Born at Reading, Berks.
1901 CENSUS RG13/1152/107/10
Civil Parish: St Lawrence
Ecclesiastical parish: St Lawrence
PHILLIP G STEER
Son of The Rev. Thomas R. Steer and Kate Steer, of "Fircroft," 66 Shinfield Rd., Reading. Native of Swanage.
Royal Fusiliers "A" Coy. 17th Bn. 5716
FRANK G WEIGHT
Son of Henry Amos Weight and Florence Harriet Weight, of 42, Curzon St., Reading.
Royal Engineers32nd Div. Signal Coy. 103117
http://www.cwgc.org/search/casualty_details.aspx?casualty=335989Milly