Davies was crowned as a bardd in the 1951 National Eisteddfod in Llanrwst for composing the winning poem Adfeilion ("Ruins").
His other literary output includes the elegy Hedydd yn yr Haul ("Skylark in the sun") (1969) and the epic novel Marged (1974).
During World War II, Davies worked at a colliery in Oakdale near Caerphilly, as a Bevin Boy.
Davies had four sons, including the composer and broadcaster Gareth Glyn and Geraint Glynne Davies who is a member of the Welsh folk group Ar Log.
In 2011, Welsh television channel S4C announced the T.Glynne Davies Scholarship for the year 2011–12.