The Met Office said remnants of the hurricane, which hit New England in the US and eastern Canada, would particularly affect parts of west Wales, Cumbria and the Pennines, with a yellow rain warning in place. It will no longer be a hurricane by the time it reaches UK shores. Strong winds will also pick up across England and Wales, with coastal gales developing in the west.
It comes after thunderstorms in the south-west of England on Sunday led to heavy rain and flash floods. A Butlin's holiday resort in Minehead, Somerset said it would be closed for four days after its site was damaged by the torrential downpours. Exeter Airport was also forced to close and cancel its remaining flights on Sunday.
The Met Office said showers were "highly localised", with the airport seeing 57.4mm of rainfall, while Swindon in Wiltshire received 90.7mm overnight, with the average rainfall for the entire month of September in the county about 61mm.
These showers have since shifted to areas in the East Midlands, with Nottingham and parts of Lincolnshire seeing 40-45mm of rainfall on Monday.
About 10,000 lightning strikes were recorded across the UK on Sunday, with a further 800 recorded across Yorkshire and North East England on Monday.
Dan Stroud, meteorologist at the Met Office, said: "We're undergoing a change at the moment, we've got a cold front moving in from the west, so that is helping to clear out all the showers and thunderstorms we had yesterday which have been shunted eastwards out into the North Sea."
Looking ahead to Tuesday, the forecaster said conditions would be mostly cloudy with an area of rain moving in from the west, with a yellow rain warning in place for parts of west Wales, Cumbria and the Pennines.
The best of the weather will be in Scotland, which will be cloudier but with lighter winds.
Windy conditions are likely to continue on Wednesday but will gradually ease.
The Met Office added there would be more focus on blustery showers and sunny spells on Thursday and Friday, with a "generally unsettled" outlook over the next week or so.