The award of Pte Bigley's Military Medal was announced in the London Gazette on 25 Jan 1918, page 5, in a long list of similar awards, with no citation, other than the standard heading 'for bravery in the field'.
He is listed as 3/5724 L/C (A/Cpl) W.Bigley, E.York.R, (Jarrow).
A local newspaper is usually the best place to find more details of these awards, or possibly the war diary of Bigley's unit, which is likely to be at the National Archives, Kew.