Would that be into the car I was overtaking (to my left), or head-on into the car he was moving out to overtake (to my right)?
It's difficult to say for sure as I wasn't there to judge for myself, however, given that one of the two of you were over the double white line, that would imply to me that one of you had a lesser degree of "right of way" than the car that had entered the "middle" lane after you, I'd also suggest that applying the brakes and dipping back in behind the car you were overtaking takes less thinking about than flashing your lights at the oncoming car and expecting them to figure out what is going off before hitting you head on at a closing speed of 120mph plus ?
May I ask, what was the end result, I'm assuming by the fact you are writing about it that one of you "gave way", regardless of being in the right or not ?
I was heading uphill and had already pulled out before he came into view, crossing a single dotted line to do so. I also had my dipped headlights on as I often do in grey conditions, so as to make myself more visible.
The car coming the other way was coming downhill, had to cross over a solid/dotted double white line in order to make his move, and only began to do so when I was already up alongside the car I was passing. Even if he was calculating that I would have completed my manoeuvre by the time he met me, how did he know that there wasn't a car following me through? Moreover, the lane I was in is used by traffic turning right at the next roundabout, so it was quite a cheek to expect me to get out of it.
I was so dumbstruck by his manoevre that I applied full beam lamps to deter him (they are less dazzling during the day than at night, and the Highway Code recommends their use as a warning anyway; my only fault it that I turned them on, instead of just flashing!). I continued to out-accelerate the car to my left so as to complete the manoevre, as I would have had to brake very hard to drop back in behind the car I was already passing, and I couldn't look at it because I didn't dare take my eye off the car coming the other way!
The guy coming the other way was in a whole stream of traffic, and would never have passed more than one or two cars anyway, even if I had not been there. He was still pretty insistent on coming out, though.
In the end I had to pull across on the car I was passing, which I had fortunately cleared. I and the guy coming the other way ended up passing each other straddling the respective sets of lines towards our own side of the road (as a crowd of parked truckers in a layby watched on!). When I looked in the mirror he had aborted his manoevre, and retreated to his place in the long queue he was part of.
I have no doubt that I was in the right on the grounds that I was going uphill, had only crossed the single dotted line, was already making my move when he started his, and was using a lane which automatically became "mine" a few hundred meters further on, whereas he would have had to get out of it anyway before he reached the next roundabout.
If you want to know where it was, it was on the A361 S2+1 heading from Frome towards the roundabout with the A36 at Beckington.