Thanks to Tana of Small farms, I went to check out some blogger settings.
I found out about the word verification option.
(found under blogger->settings->comments)
I have instigated it for this blog, hopefully it will get rid of the spammers.
If it doesn't work, we can add a registered users only option.
(where only blogger registered commenters can leave comments)
Failing that we can go one stage further and only allow blog members to comment.
I would prefer not to have to go that far.
But we'll take it one step at a time and see if this first step eliminates the spammers successfully.