>If I said I was going to town, it would carry a different meaning to going to the town: the latter meant the local town, the former meant going up to London<

When I lived in Leeds (Yorkshire, northern England) 'going to town' was not used in a geographic sense, only in the sense of splashing out. We used to 'go into town' if we went to the city centre.
AS for London, I think we used to go to London. I don't recall an up or down in the phrase.

On the other hand, when I lived in Harpenden (southern UK, just north of London) and we went into the town centre, we went 'down the village'.

(As an aside, what does it mean that we talk about towns when we mean cities, and villages when we mean towns?)