Okay... That didn't take long.
I have found something called Debut by NCH Software (registered in the USA and Australia).
They have a free version and a premium version which costs about $30.
http://www.nchsoftware.com/capture/index.html It works, although I'm no expert on this kind of software, but it recorded both the VSTi window and the Console view just fine.
It does not, however, record audio played by my ASIO device, but I'm not bothered about that. I'm going to use a video editing package to splice the audio and video together.
The same company has a video editing package called VideoPad. It does not appear to be free and is currently priced at around $40, and I've only just noticed that there is a deal on until the end of May, so once that runs out the cost will rise considerably. I'll probably give this a miss because there appear to be plenty of open source video editors out there...