Hi. Thanks for the reply.
I've asked my wife to keep tabs on when it happens.
Things I can answer:
We're in the UK
Her mobile provider is Orange
Our ISP is Virgin Media - but this has happened on WiFi at home and at her father's address where the ISP is BT.
One of the websites that was being browsed, in Safari, when it happened was allpoetry.com
One of the weirdest things, and I've yet to fully understand this bit, is that it appear to take her away from Safari to deliver this content - but I don't understand how that can be. When she returned to Safari, for example, this content wasn't there, but the allpoetry page still was. I also couldn't find anything that appeared to explain what site it could have been in her browsing history. So it was like she hadn't actually seen it on a website at all!
I'm told it also happened when she was using the Words with Friends app from Zynga - on this occasion she was using the game, and put the phone down when our kids came looking for her. She picked it up moments later, and this was there. This app does serve up ads in between turns, which would lend itself to the ad server theory. But surely Zynga must be cautious enough about their rep to not allow this kind of ad to be placed?! ... I also use this app, and have never had this problem. But then I close the ads as soon as they pop up, whereas on this occasion it could have been allowed to run long enough to redirect somewhere else ... Though still surprised and shocked.
Afraid to say I don't understand the suggestion re OpenDNS. Don't understand what it is, or how I'd use it. Sorry.
I'll post any more information I find if it happens again.
Guess I'm not surprised by your comment about Apple not reading these sites formally. But I can't believe that no one connected with them wouldn't note this if it started to get a lot of traffic, and a lot more people reporting the problem. They appear to pride themselves on being family friendly, not allowing dodgy apps, and being virus free! I won't hold my breath though. I suspect you're right, and I'm being naive.
Thanks.