Yesterday I noticed that when I clicked on links to other pages within my blog, one of those nasty little messages popped up asking if I was sure I wanted to leave this page.
The page within my blog then appeared, but shortly thereafter it automatically redirected to a dating website.
I queried this on the forum - turns out third party gadgets are causing the problem.
In my case, it was the calendar - now I have removed it, all is well.
So, if you are having a similar problem, remove any spammy gadgets like the calendar, and apparently there's a Facebook ad gadget that is also causing this problem.
As Blogger is owned by Google, I really think they should investigate gadgets before making them available to users!