My car has developed this weird noise when I set off from a stop or accelerate. It is more noticeable when going up hill. Any ideas what it could be?

The shaking noise is just the camera vibrating.

Here is a video which is a compilation of a few clips where you can hear it.
http://www.youtube.com/watch?v=9UuvJlqKEeQ

Sounds like a rattling exhaust perhaps? Also check the airbox is secure, that often causes rattles.

I think the back box may be a little corroded, could it be that? It does sound like it's coming from the front though.

Check the pipe on the airbox, it should be connected to the bracket? If not, cable tie it back on to the bracket and see how it is! Thats all my problem was

exhaust heat shield maybe

I've not yet been able to check your video but if it's a rattle then my experience on my 1.2 might help. I had a rattle at low and high revs. In the end I tracked it down to:
1. A loose airbox inlet pipe where it goes through the mounting. Like many other people - sorted with a cable tie
2. Exhaust. Two things: i. a broken (rusted to death) clamp where the exhaust was mounted just under the front of the engine; ii. when I removed the exhaust pipe I tipped it up and emptied a load of rust that seemed to have got stuck somewhere between the downpipe and the silencer
3. And this one made the most difference(!) - the dipstick was rattling against the sump from the inside. A quick straighten of the bottom part and silence......

Been about 10k miles now since I did these and they haven't returned yet