To supplement the previous answer - coffee, tea, herbal teas and fruit juices are all available 24/7 from the Kings Court area of the promenade deck, Deck 7.
There is no charge for room service tea and coffee and meals on the QM2. All part of the service. Not sure about charging for other beverages though.
Rome service is available 24 hrs all you have to do is pick up the phone. sorry I don't want to sound rude but why pay all this money and then want to make your own pot of tea ? your there to be pamperd go on and have everything that going and sit back and enjoy your self.. don't worry if it's three in the moring and you want that cupper just pick up the phone.. thats about the time I'm just rolling in from the night club and I pick up the phone and order a nice club sandwich they are more than happy to serve you.pau.