The Thames tide timetables are published by both the Port of London Authority (PLA) and the British Hydrological Office.
The PLA provides data specific to the estuary and has tables for 2013 on it’s site. You can also download the pdf of the timetables for 2013 They can also provide predictions up to 2015 if you really like to plan things in advance!
The PLA constantly monitor the tide and so provide live data of what the river is doing right now. Predictions are obviously just that and the amount of rainfall into the Thames catchment makes a big difference.
The British Hydrological Office gives you tidal predictions in wonderful graphs that let you see how the rhythms of the tides work and is well worth looking at.
The most detailed work on what the river is doing right now can be found here The graphs are in real time and show how the tide is now and how much it varies from the prediction. The whole Where Thames Smooth Waters Glide site has lots of Thames related information and is worth the effort!