Hi

His death registration says that his parents are John Alfred JEFFREYS mother Jane THOMSON

FreeBMD UK
Marriages Sep 1882
JEFFREYS John Alfred married THOMPSON, Jane
District: Sunderland County: Durham Vol: 10a Pg: 808

Here is birth of Leslie and his siblings parent John & Jane in NSW
32961/1884 JEFFREYS JOHN A Father: JOHN A Mother: JANE
District: WENTWORTH
30282/1886 JEFFREYS ROBERT S Father: JOHN A Mother: JANE District: HAMILTON
5215/1888 JEFFREYS LESLIE G Father: JOHN A Mother: JANE
District: LEICHHARDT
18586/1890 JEFFREYS JENNIE W Father: JOHN A Mother: JANE District: LEICHHARDT

Cheers
Tania