You can get the raw numbers from the web site of the Port of London Authority (PLA). Here you can find both tide forecasts and live data from gauges along the river. But they are a bit dry, and it can take time to work out the picture along the estuary.
So I was delighted to find this site that shows all this information graphically. If you look at the pictures above and below you can see the water flowing in and out of the Thames today.
Symbols show the locks upriver and the Thames Barrier in the middle, complete with which spans are open.