Kay is correct, "Yeah, nah" and "yeah, no" (varies with speaker's pronunciation) are used in London in general; as is the reverse of "no/nah, yeah" e.g "nah, yeah I was telling him, but he didn't want to hear it."
I use both myself, "yeah, nah" a lot more frequently than the reverse, and so do many of my friends and peers. I had no idea this was seen as a chiefly Australian speech habit until very recently. This is the only post I've found on the internet acknowledging that it is used in UK speech, and for some reason it doesn't seem to have been acknowledged even though it is accurate.
I couldn't tell you who "came up with it" first, but I wouldn't be surprised if it developed independently, as the thought process underlying it is apparently the same in both my usage (which I will generalise to <30-year-old "Multicultural London English" users) and this Australian reddit user's usage
the first word indicates 1 of 2 things
if they start with yeah = I hear what your saying and
if they start with nah = In all seriousness though
and how they end it is the answer
nah, yeah = in all seriousness the answer is yes or in all seriousness
i agree with you
yeah, nah = i hear what you are saying and i dont agree or yeah i am aware but the answer is no
Literally, the way he described it is a perfect transcription of what's going on in my head when I use it. I don't remember "learning to speak this way" from anyone in particular, or putting it on deliberately. I wouldn't have been talking that way in primary school. I'd say more around mid-to-late secondary is when my speech would have developed that bit further to start verbally acknowledging the other person's point of view, for example, with a "yeah" before saying "no/nah" and giving my opinion. I don't think I would need to have heard that off someone to have started doing that, which is why it wouldn't surprise me if it developed independently in both UK and Australian/New Zealander English. I wonder if it's used in South African/Zimbabwe English as well?