Some parts of the country could see a month's worth of rainfall in a single day with the wet weather to last well into the week.
Many areas of the UK will be hit by wet and windy conditions with temperatures cooler than average for this time of the year.
The Met Office has issued four yellow severe weather warnings for rain, saying that areas affected could see local flooding and disruption to transport.
The first is in place from 4am on Monday until the end of the day and covers an area from the Humber all the way down to the south coast, and from the East Midlands to Portsmouth.
Many areas will see some 20mm of rainfall, with between 40mm and 60mm falling in some isolated spots.
The average monthly rainfall in June for south-east England is about 50mm.
Met Office forecaster Simon Partridge said: "There is the potential some spots could see a month's worth of rain in one day.
"It will be fairly localised with a number of other places seeing nearly half of month's rain – so a very wet day."
Top temperatures in the South East are expected to creep up to just 14C or 15C, some 6C or 7C cooler than the average for this time of year.
The band of rain will move slightly north and west before settling, with Northern Ireland and Scotland expected to see the best of the weather, staying mostly dry with sunny spells, while areas under the rain band remain a cool 13C to 17C.
Weather warnings are in place for the whole of Tuesday up until midday on Thursday for north-eastern England down to the Wash and as far west as the West Midlands.
Many areas will see around 20mm of rain with some places getting up to 60mm.
Mr Partridge said: "A number of spots around could see, within a few days really, a month's worth of rain, so a wet, windy, fairly cool week for most."