The short answer, is there isn’t a lot to do in December!
The long lasting warm temperatures this autumn meant that leaves have stayed on trees for longer than usual. You can rake these off the lawn, but it’s worth noting that this should be done on a dry, frost-free day, so as not to cause any unnecessary damage.
Any worm casts that have appeared can be moved on using a good stiff brush. This job should also be undertaken on a dry day.
Take a look at the lawn mower and make sure everything is in working order. Pay particular attention to the blades. Read more on that here.
If all else fails, you could always take a browse through the Lawn UK Christmas gift range.