Well that's kind of the point isn't it?! If £17 gross was genuinely the average wage you wouldn't have to crawl through ads for hours! They'd be easy to find. They're not easy to find because that figure isn't accurate.
The first one you link to says £15 an hour, no indication if this is net or gross. It's also a parent post (possibly a parent who, like you, doesn't know the going rate), not an agency who will have a more full idea.
The second link you post is for an agency called Tinies who are a UK-wide company. It does say £15 on that link, but if you scroll down on that same page it also says "an experienced, talented nanny may demand a wage as high as £25 per hour". It then goes on to list things that might impact salary, the top one being location i.e. a London nanny will cost significantly more than one elsewhere.
Again, if £17 is average it will be easy to find an agency offering jobs at £17 an hour (and also significantly less than that to make the average work).
I think your faith in the nanny tax figures is a tad misguided, as hopefully you can now see from your own research.