I probably won’t remember all that has been found but working back from the military record for your John:
11th July 1889
John Egan, born Pancras gives his age as 20 years, 2 months.
This would give his birth year as 1869.
The same record gives father as Timothy Egan, 10 York Buildings, Euston Road and also then mentions wife Alice and Margaret Primrose.
1914 his age is 44 yrs.
I have not found his birth - have you? We have b 1867, I think but these records are more 1869.
1911 census - 45 yrs (abt 1866)
1901 - 33 yrs (abt 1868)
1891 - army?
1881 - 14 yrs abt 1867 with Timothy and Margaret at Cleveland Street
1871 - 3 yrs abt 1868 with parents and brother Michael
** do you have Michael’s birth?
If those births were found, you would have the mother’s name.
If you purchased the marriage for Timothy and Margaret Mannix, you could check the details there.
Similarly, do you have the marriage of John and Alice?
I have it gone back through the thread but I know there is more detail.