I'm guessing that on morning of Jan 1 LHR will be relatively quiet; but in general coming in from a US overnight I would recommend going to the T5 arrivals lounge for shower, because there are about 3x more showers than in the main departures lounge so you will not have to wait. In the departures area (CCR) then you will often need to wait for up to 30 minutes at busy times to get a shower slot.