I must admit seeing adds would make me think it's not a legit site.
You've hit it on the head there, that was my first thought!
Or had my device been compromised? Once the initial panic subdued though it turned out to be just ads, probably from Google as it was throwing up things that would have been triggered by recent searches.
I doubt if they are doing anything illegal, they'll have thought it all through. Time was, and not that long ago, I'd have composed a formal complaint and seen it through to whoever is in charge. But these days I try to be more relaxed, and just having a mumble and a grumble on an Internet forum is so much less stressful.
Off-topic since it's not gov.uk, but another thing that's been ruined by ads recently is National Rail's smartphone App. Used to be one of my favourite Apps, but in the past few weeks it's gained prolific ads, pretty much ruined it.