I am looking where you have said, where you specify server name, sender, etc and there is no SMTP authentication section (I have Googled and seen a screenshot, it doesn't show that bottom section in 10d).
I think I may have solved it though! Shall report back tomorrow when I can confirm :)
It was set to a maximum of 1 alert per 1 minute and for some reason this was stopping any going through, not just 1. Increased it to the default 5 per 5 minutes and test job runs now work (which weren't before, just the recipient test was working).
Thanks for the help.
Michelle