I think Aghadowey was clarifying the Barrow person was someone else.
Is not buried in he City Cemetery and unlisted in Shankill cemetery (incomplete). The body may have been returned to father. Per the Effects entry his account was managed at Woolwich.
Using Findmypast the 4 or 5 Thomas Brady's with father John on 1911 census in England all seem to be alive 1921 still with parents per their suggested records (the Barrow Thomas married with wife Agnes).
The Thomas Henry born Durham Q1 1902 died same quarter.