Ok, firstly here are a couple of pictures of the first design I came up with. One is the front view and the other is taken from the side.
As you can see, it doesn't look much like a tea cosy at all, but to get the gaps for the spout and handle, I just slipped the slip stitches on to a separate needle and knit the 2 sets of stitches separately for a few rows before rejoining them on the one needle.
GG, decreasing in double-knitting is fiddly, but increasing can be more straightforward. The best method I found was to make a stitch by lifting the running thread below the next slipped stitch. I forget exactly how I got the increases on both lots of stitches, but found this helpful: http://www.knittinghelp.com/forum/showthread.php?t=74430 and also this: http://www.stitchdiva.com/tutorials/double-knitting/make-one-increase. I have scribbled notes somewhere to assist me - if I come across them I'll pass them on.
I cast on about 4 stitches and knit a couple of rounds before doing increasing, which I did before making the gaps. Again, I have forgotten all the details - I should have written it down at the time - can't you tell I'm a novice at designing lol? I think I knit a couple of rows straight before binding off tubular/double-knit style.
Here is a picture of the result - looking slightly more like a tea cosy.
I have not yet figured out how to apply what I have learned to a normal-sized tea cosy, but will post here when I have.