I have located an 1851 census for William McAra mistranscribed as McAree, soldier age 21, 33 Regiment, born Stirling Scotland. As an Artificer he could be a soldier and would explain why he moved to Plumstead, location of the Royal Arsenal.
I have found a marriage for a John McAra and Mary Maxwell 27/04/1831 Parish Stirling County Stirling
No   Date   Surname   Forename   Spouse Name/Frame No   Sex   Parish   City/County   GROS Data
19   27/04/1831   MCARA   JOHN   MARY MAXWELL/FR1618   M   Stirling   /STIRLING   490/ 0070 0073
Also found a birth for a John McAra but it looks like the family moved Crieff and had several other children
No   Date   Surname   Forename   Parent Names/Frame No.   Sex   Parish   City/County   GROS Data
23   16/04/1810   MCARA   JOHN   ALEXANDER MCARA/JEAN MCEWAN FR1500   U   St Ninians   /STIRLING   488/ 0040 0201
Any help or ideas would be appreciated, I have tried to find military records but no luck.