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Sadly after more than a year, the National Archives are not able to provide the details of William Wright's enlistment into the 5th Foot Regiment.   They were in Ireland at the time, 25 January 1782.
Nor can I find his demob or death as a member of the 24th Regiment of Foot probably early in the 1800s.
Does anyone have any ideas?
Thanks
John

I have discovered that an ancestor enlisted into the 5th Foot on 29 January 1782, when the Regiment was in Ireland.   The museum at Alnwick have been very helpful, but their early record book dates from 1800. Can anyone help me to find out more about William Wright, who I know was still serving as a corporal in 1806, albeit in the 24th Regiment to which he and the rest of the soldiers and corporals of the 5th Regiment had been (compulsorily) transferred in Quebec 25 June 1797.
He married Ruth SNU and they had an infant son William who died in Quebec in 1796 and a son Munday born Quebec 1797. Looking for William senior's date and place of birth and anything about his ancestors
  Thanks.

Thank You Max.  I hadn't realised he had joined DCLI first.

Thank you Skoyen 89 and Max for your efforts.  Addictive is the right word!  The detail from Major Shand's diary is compelling and probably supplies the real clues as to William Brown's demise -there are several passages that describe losses.   Also found another source - the written account of Lcpl Richard Seddon RAOC in "Retreat: Dunkirk and the Evacuation of Western Europe."  Seddon also provided the Imperial War Museum with some verbal recollections.   Putting all of that evidence together, it is likely that William Brown is one of the 63 unidentified British soldiers at the St Valery en Caux Franco British War cemetery "Known unto God".   

My Uncle was 7581797 Cpl William Brown RAOC, missing presumed KIA June 1940 whilst attached to the RASC supply Column 51 Highland Division.  Is there any way of finding out how the CWGC got the info on him?