It's happened quite a bit over the last few days for me when using Safari on my iPhone. I've assumed it's something that's hidden in or hijacking the advert banner.
Anyone seeing such messages should probably at the very least immediately close the browser window, avoiding clicking on any buttons that are part of the pop-up, even buttons for close or cancel.
For me clearing cache isn't a lasting solution. Within minutes of clearing the cache a couple of nights ago it was happening again. Been OK the last couple of days for me.
Not sure how easily it could be stopped or even investigated as we may all be seeing different adverts that are based on our recent browsing. I placed an order online with Zavvi for the first time in a while the other day so now I'm seeing Zavvi adverts all over the place, usually (and pointlessly) showing me that they sell the specific items I've just ordered.
On my phone right now I've got an advert saying 'HBX Sale' at the top. Not sure what that is. I don't pay these banner ads much attention at all but my recollection is on my phone the ads are rarely for sites I do visit and shop at.
I'm writing this on my desktop computer just now and I've got yet another Zavvi at the top of this page. There are Norton 360 adverts at the bottom, would be a bit ironic if ever those were the ads where these nuisance pop-ups spring from.
I got one or two very recently on this forum on my phone, the same Samsung user messages as lj. I go through phases of getting them, for a while I kept getting them on The Guardian website, but not so many recently.
I'm wondering whether it's malware rather than any specific site.
I used to have a similar issue quite frequently on another site entirely, though the only time I ever had it happen was on my phone, never my laptop. I ended up having to install adblock software on my phone to be able to use the site at all (which I do frequently).