As I’m sure everyone is aware, the Environment Agency displays stream warning boards at locks when the river flow reaches certain levels. When red or yellow boards are displayed the EA advises unpowered boats (i.e. us) not to navigate.
As these warnings are advisory, rather than mandatory, you will need to make a decision on whether or not you paddle when the warning signs appear. You can check the current conditions on the EA website here: https://www.gov.uk/guidance/river-thames-current-river-conditions.
As each warning board covers a wide range of conditions and flows, it might be more useful to look at river flow rates. River flow is measured in cumecs. 1 cumec = a cubic metre per second flow.
This webpage summarises a lot of useful information include warning boards and flow rates: https://andrie.quarto.pub/river-thames-conditions-at-hampton-court/#times-of-sunrise-and-sunset
Check out the HCC page on river flow for more information: https://hamptoncanoeclub.org/staying-safe-on-higher-river-flow/