I haven't done this for a while, so I apologise for the lack of detail. You'll need to go into the source code for the web pages you're loading and look for the code that's loading the video - it'll be something like xxx://www.server.com/videofile.ext. The xxx part is the protocol that's being used to stream the video, but I can't remember what the options are.
Make a note of it and then Google for 'xxxx' and 'download' - you should find several apps that can capture streaming video.