Hugh was the son of Henry Annett of Widdrington, Northumberland, and Edith Annett (formerly Crawford) of Stanton Fence, Morpeth. He was born in 1886 in Widdrington and had three siblings: Henry (born around 1884), Edith (born around 1888), and James (born around 1890). His younger brother James also served with the Durham Light Infantry and survived the war. Three staff also shared the Annett family home; Maud Burland (the Governess), and Mary Ray and Isabella Morton (both servants).
Hugh was educated at King Edward VI School, Morpeth, then Armstrong College (1902-1906). At Armstrong College, Hugh studied Metallurgy, Mining, Surveying, Engineering and Electrical Engineering and was awarded a BSc in September 1906. He worked as Under Manager at Horden Colliery having gained his manager's certificate in 1909. He was also a member of the Institute of Mining Engineers.
Hugh joined the Durham Light Infantry, 6th Battalion on 14th July 1915, gazetted at the rank of Second Lieutenant.
Hugh arrived in France on 15th March 1916. On 6th June 1916, he led 24 men in Y Company in a night raid against German trenches, but came under heavy resistance from opposition troops whilst in no man’s land. The delayed raid was attempted again on the 9th June and once more on 12th June. Hugh and his men entered the enemy trench, and after doing considerable damage with bombs and rifles, returned without casualty.
Hugh was killed in action aged 29 whilst leading his company. On 15th September 1916, Hugh's battalion joined the 151st Brigade's assaulting formation at the Battle of Flers-Courcelette (15th - 22nd September 1916), near Martinpuich (Battle of the Somme). At 6.20 a.m. on the first day of this assault, his Battalion moved from Shelter Wood to the South West corner of Mametz Wood. At about 4 p.m. word came that the Battalion would move up the line at once and a conference was held with all Company Commanders. The Battalion attacked the German trenches, but were unsuccessful.