Battle of the British Standard BS3621
The classical way you handle this situation is to pull the old part out and take it to the store, precisely so you can compare dimensions and show it to a clerk to tap his experience. 

You prefer mail order.  That works much better if sizes are standardized to one size, because then, you would not have to learn things about lock fitment. As a direct result, you have formed the expectation in your mind - because that is what will work the best for you.  

It's like "surely the speed limit must be 120kph, because I'm late".  

That is why you are concerned with BS 3621 - you desire size standardization to exist, you hope there is a standards document that calls it out, and so you latched onto (heh) the first standards document that seemed to relate.   It says nothing about lock dimensions. 

I recommend you make yourself a sceptic of thought processes like these so you can stop being snared by them.   

Also I suggest you run, do not walk -- I mean walk, do not type to the nearest appropriate hardware store, old lock in hand, and have the clerk help you, then cheerfully pay his retail price for the needed part.  While this will be more expensive than 1 mail order lock, it will certainly be cheaper than "education via buying the wrong parts". 

P.S. I just spent a half day fiddling around with a fuel pump which arrived with the wrong fittings necessitating a fuel line  reroute, and the bar was  bent wrong so it wasn't even touching the eccentric (hence not pumping). A quick search of the Web reveals all modern fuel pumps are similar.   So I feel your pain.  I would have much rather just walked into the Stihl dealer, however this is not a Stihl.