Pare down the buying list: we buy for our DC, niece, nephew, 2 godchildren of DH's and that's it. We don't buy for each other, pointless.
Therefore wrapping is a doddle. DC's gifts are wrapped in fabric and ribbon, and fabric drawstring bags, I have made many in different sizes and shapes. I made initials out of air drying clay one year, a whole heap, so they're attached to the ribbon as they're wrapped. Takes about 30minutes tops!
Christmas cake is made at the end of September. As are Christmas cards (I'm an artist), so when October hits and we get really busy, I don't have to worry about making and then posting them (we're abroad, things get posted December 1st).
We don't do a traditional British Christmas lunch, so I'm no help there.
We don't try and cram in every Christmas thing going: panto, visiting FC, Xmas market, nativity play, watching the town lights go on etc. We'll do one or two things, but not all of them, too exhausting.
RACKing is also something we do: Random Acts of Christmas Kindness. You can choose anything you want, take your DC's lead.
Even when we did do big Christmases, I found just jotting down stuff in a notebook was organisation enough.
I would suggest, however, having a separate purse (or make up bag, whatever) to keep receipts in for things that could be faulty, duplicates etc. I use it religiously and it's so handy to have things in one place.
...BATTERIES! You can never have too many batteries!