The speakers in my iPod Touch have failed after just one month and although Dixons have refused to replace the item as I've had it for more than 28 days I've written to them quoting the Sale of Goods Act and know that I will eventually get a replacement as their 28 days clause has no legal standing.
My concern is, what happens to the applications/music I've purchased and downloaded from iTunes? When I eventually plug in the new Touch will I be able to transfer the applications etc. to the new hardware?

Yes. I got a replacement from Argos after I arsily took it back because of a couple of dead pixels, and was able to associate iTunes with it fine and retransfer files to it. It doesn't count as an authorisation or anything.

You've got a 12 months warranty from Apple when you bought it, no matter who you bought off. I've bought 2 iPod Touch (one off eBay the other from Amazon). Both developed a fault, so I just took them to my nearest Apple Store and in both cases got replacements within minutes.

Legally, they could just send the iPod to Apple (they reserve that right).

If they go down that route, it would be a lot quicker to do it yourself.

As for the content, you'll be able to sync everything that is in your iTunes library.

If you purchased something on the iPod touch and it wasn't copied to your computer, you can contact Apple Support and they should let you download it again.