Here are some hotels near Tate Modern that come recommended:
Mercure London City Bankside - now sold out of Tate Classic rate!
The Southwark Rose Hotel - should still be offering rates of £133 per night (inclusive of VAT and B&B) for Tate attendees; please contact Amber McClory or Gabriela Salgado at Tate who need to let the hotel know you are with us.