Sources

The list of names of men with the Brierley surname was derived from the Commonwealth War Graves Commission. The CWGC website gives data including surname, forename (or initial), rank, service number and service (regiment and battalion), date of death and location of cemetery or memorial. In some cases, the data also includes names and address of next of kin.

Biographical information is derived from Census data available on Ancestry.

Ancestry also holds military databases:

UK Army Register of Soldiers' Effects (the most useful source of information re the soldier's next of kin)
UK Soldiers Died in the Great War (shows date of death, place of birth and place of enlistment)
Most service papers were destroyed during the Blitz but some have survived: British Army WWI Service Records, 1914-1920; and British Army WWI Pension Records 1914-1920
British Army WWI Medal Rolls Index Cards, 1914-1920 (if the man served abroad in 1914 or 1915 the card shows the date they landed and the theatre of War)
UK, WWI Service Medal and Award Rolls, 1914-1920 (shows final regiment served in and also any previous regiments or battalions).
For those with special awards: UK, Citations of the Distinguished Conduct Medal, 1914-1920; UK, British Army Recipients of the Military Medal, 1914-1920
For men invalided out of the War: UK, Silver War Badge Records, 1914-1920

The essential source for information about army formations (Divisions, Regiments, Battalions) and an overall picture of where each battalion fought, is The Long, Long Trail.

Wikipedia is a good source for finding out about the various battles. The best place to find information about where a battalion was on a specific day is the battalion's War Diary. These can be downloaded at little cost from the National Archives.