The previous post about the depth of the Thames considered the depth when the river is at its shallowest. Of course there are big variations a couple of times day, as the Thames is a tidal river.
The depth of water at any particular time can be calculated by adding the current depth of the tide to that of the underlying chart datum. The various concepts are shown in the figure below and described on the Port of London Authority site here.
You can get the tidal range from a number of sources, my favourite being Easytide which can be found here. It gives plots of the tide against time for up to 6 days (free) adjusted if required for summer time, and also the times of high / low water and the sunrise / sunset times. As well the standard ports it even does points on the river such as Hammersmith Bridge (as shown in the figure at the top).
So if the chart datum is 2m and the water height for now is about 4m, then the current total depth of water is 6m - simple!
There's a lot of other resources available - in particular on the PLA site which includes time tables at this site here.
Of course these are predictions, and the reality can be very different. Atmospheric pressure varies depending upon the weather - something we have a lot of here - and effects the height of water in the river. A massive storm with low pressure in the North Sea can push a wall of water up the estuary.
And you can watch this happen, as there are live tide gauges on the internet, so you can compare predictions against the reality - cool!
To get a great feel for the great range between high water and low water, watch this time elapsed film