The Met Office yellow (be aware) warning is from 9pm on Sunday (April 29) until midnight on Monday (April 30).
The report says: “A period of heavy rain will affect first South-Eastern England and then parts of East Anglia on Sunday evening, lasting through much of Monday.
“Although there is much uncertainty in these rainfall totals and how far west the heaviest rain will occur, accumulations of 25-40mm are possible, and 50-70mm in places during this period.
“The heavy rain will be accompanied by strong to gale force northerly winds, and it will be cold enough to produce some snow on high ground such as the North and South Downs, although this is unlikely to settle.”
The Met Office adds: “There is a small chance that homes and businesses could be flooded, causing damage to some buildings.
“Spray and flooding could lead to difficult driving conditions and some road closures.
“Where flooding occurs, there is a slight chance of delays or cancellations to train and bus services.”