[clivehawkins]

I'm confused.

Doesn't continue mean 'to do the same thing' ie not change activity? The very idea of using the verb continue to indicate a change in activity seems a bit odd to me.
In Mark's example he correctly states 'She continued to ignore me' means she was ignoring me, and then carried on ignoring me, hence no change.

I suspect, and I may be wrong (as I so often am), that there may be some confusion with 'Go on', which is a synonym of continue, although with a slight but important difference.

For example:
Peter went on talking for most of the afternoon. ie he continued talking

Following the introduction Peter went on to talk about a variety of interesting subjects. ie changed argument.

After cooking lunch, Mickey went on to wash the floor and tidy his bedroom ie he changed activity.

The teacher told the class to be quiet but they went on talking, much to her annoyance. ie they continued the same activity.

At least that's how I've understood it.

Anyone else?