Upvote:1
There are the Hilton Hotel in Terminal 4. Accessible via a walkway from Terminal 4. They have Day Use Rooms available with access to their lounge included.
Sofitel in Terminal 5 which is accessible from within the airport.
There are showers in Terminal 3 departures according to the Heathrow Airport website:
Showers are available in the No.1 Traveller Lounge in Terminal 3 departures (after security) – there is a charge for entry. Facilities may also be available to eligible passengers in the airlines' own lounges.
You need to pay to access the lounge, which can be done online. I don't know if you can do it on arrival.