Okay, so I've had a chance to read that and it's an interesting one.
On the one hand they (the Ombudsman) are saying that insurance companies cannot penalise you for spent convictions, which is why they ask you for up to five years' worth of details (for totting purposes it's 3 years, after 4 you can have them removed from you licence, but they're not officially spent until 5 years). A speed awareness course (SAC for the sake of brevity) is not a conviction, and as such I would say that, based on that Issue 25, you do not have to tell insurers about SAC as they are not allowed to penalise you for it.
However...
They are allowed to penalise drivers who have had a claim, regardless of fault. They are allowed to penalise drivers who have had a speeding conviction. As such, why should they not be allowed to penalise people who have clearly been caught speeding? Points or SAC, the crime is identical and should be treated as such. On this subject I'm actually going to side with the insurer I think, and I would be interested to hear the opinion of the Ombudsman on this subject now, given how popular SAC are in lieu of points and that the article Haydn linked to is 9 years old.
I might drop them a line and ask.