The agency urged 85 communities in England and Wales to be on alert as heavy rain hit parts of East Anglia and the East Midlands this morning.
The Met Office also issued an amber warning that advised people to “be prepared”.
The east and northeast of England are expected to be worst affected, as two bands of heavy rain are set to soak the regions today and tomorrow.
BBC weatherman Peter Sloss said that the worst-hit areas could receive as much as 60mm of rain – the average monthly rainfall for July.
Yet more heavy rain is forecast for the weekend in parts of northern England and central and southern Scotland, again with the potential for flooding.