I sent off my sons passport for renewal on New Years Eve and got the new one
back on 5th January, really quick, so apply now for a new one, its worth paying the extra £4 at the post office for their checking service, its really quick!
i'm in exactly the same boat. i'm going at the end of January and mine runs out in April I will have to pay quite a lot and make an appointment at the passport office I think.