Received a rapid reply:
"Thank you for your enquiry.
I have taken advice from my colleagues within the Met Office Flood Forecasting Center who have advised me that they are constantly monitoring this and many other situations within the United Kingdom and at present, the likelihood of this event is of low probability. The Met Office and the Environment Agency are in contact 24 hours a day and if situations do call for any precautionary action to be implemented, please be assured teams across the UK are kept informed.
For information on the Thames Barrier and its operational status, please direct any questions to the Environment Agency's press office at the following address - email@example.com
or by phone on 0207 863 8710.