Assuming nobody's been super helpful in the meantime, and being bored today, I decided to help you out by knocking some together myself.
http://home.vis-is.co.uk/data/weather-icons/weather-icons.jpg
Like the one's you linked to, they're based on the old BBC ones, but with variations which are hopefully enough to differentiate them sufficiently enough to keep the BBC's lawyers away! You (and anyone else on TV Forum) are welcome to use them, for free, for any personal projects. If you're wanting to use them commercially (i.e. you make some money from their usage), contact me to arrange alternative terms. If you use them, and the BBC comes calling, I offer no support at all - use them at your own risk!
The only other things to add are, if you use them, it would be appreciated if you could give me an acknowledgement, and secondly (and this goes to everyone), please don't distribute them yourselves, and don't pass the link out to others - I will keep them available from here, so if you know someone else who wants a copy, send them to TVF to get hold of them.
You can download them from here:
http://bit.ly/dN1NXz - included are 256x256, 64x64 and 32x32 32-bit PNGs for all 32 of the standard BBC set (some are repeated in line with the list that they used to have on the weather site).
Hope this helps!