Hi Baboonboy,
At this late stage in the season, you may well have decided to lock your mower away in the shed until spring, if so you can scarify the surfice by just roughening it up a little with a spring-tine rake, select a grass seed type to suit your needs ie-'Hard wearing; 'for shady areas' etc, sow thinly over the bare muddy patches, then cover with a thin layer of general purpose compost or good top soil and if necessary cover with a piece of chicken wire to prevent any disturbance, the seed will just stay dormant until the ground warms up enough in the spring (do this when there is no frost imminent) If you have to get the mower out before germination, just mow around the seeded areas.
This task is best done after Compman's good answer!
Good Luck Tbird+