I had the same problem but was unable to fix it by dripping oil into the mechanism, so I replaced the timer. Unfortunately I bought an MI-2 timer and my 20245 toaster had an MI-7 timer in it. It looked like the MI-2 would fit physically, but the pins are numbered differently and I didn't feel comfortable guessing which one should be connected to which wire.
I emailed Dualit and their excellent customer service team sent me back PDFs showing the pin-outs of each type of timer:
http://www.gramheavy.org.uk/junk/dualit_mi-7.pdf
http://www.gramheavy.org.uk/junk/dualit_mi-2.pdf
Using these I was able to successfully hook up the MI-2 and get the toaster working again. The only thing you'll need when switching from the MI-7 to the MI-2 is a new pair of screws. I found a couple from an old computer hard drive that were the right thread and length for the job. You may also notice that the shaft is a little shorter.
Once I'd tested the new timer and confirmed that it worked OK, I set about dismantling the old one to see what makes it tick (heh). It looks like it will come apart without needing to be destroyed. Don't bother removing the cover over the pins like I did, you'll only get yourself in a mess with various springs pinging around. It's easy enough to put back together, just takes a bit of time. To get to the business side of things, remove the nut from the shaft and take off the black plastic cover as above. Now get a craft knife or flat-blade screwdriver and cut/scrape off the two tiny black plastic blobs on either side of the shaft. When you put this back together, replace these with little blobs of Araldite. With those removed, the metal guts of the timer should lift out. You'll see the spring wound round the shaft, the shaft connected to a bunch of cogs to gear down the rotation, eventually getting to a small escapement mechanism. I couldn't see anything wrong with mine and, annoyingly, it works fine now it's out in the open. Maybe a good clean and re-lube will fix it permanently and I can keep it as a spare should the new MI-2 go wrong in future.
Hope this helps!
Steve Oliver, January 2009