Availability may also have been a factor here in the decision between fitting an Aldis or a Model 1918. The latter was still current military issue at the time, whereas most of the Aldis scopes would have been recently (then) stripped from SMLE's when they were returned to Weedon circa 1921. They were one of the better Britishscopes of the era & they would also have been up for grabs on the surplus market. Aldis also continued production of the 4th pattern military type scope for the civilian market for a while after WW1, though I do not know for exactly how long. It has been suggested that they may have been using up leftovers from the WW1 military contracts.
Eric, it is more likely that your rifle was made up at sometime, but if you could tell us your scope serial number (approx would do), what the range grads are, & whether the scope has any signs of previous military acceptance/use, such as a broad arrow mark or engraved rifle serial, that would all help to give you a little more information about it.