The Met Office said thunderstorms are expected in the capital from midday onwards, with a chance of hail also bearing down on Westminster.
The weather could result in Ms Truss addressing the nation for the first time as prime minister on Tuesday afternoon inside No 10 rather than outside the Downing Street door, as is tradition.
Scotland is predicted to have a drier start before showers break out later.
In Ballater, Aberdeenshire, where the Queen is due to meet Boris Johnson and Ms Truss for the prime ministerial handover at Balmoral, thunder, lightning and heavy rain is predicted from 11am onwards.
Buckingham Palace said Mr Johnson is due to arrive at the door of Balmoral at 11.20am on Tuesday for his audience with the Queen.
His departure will, as is the custom, be private and off-camera.
At 12.10pm, Ms Truss will arrive at the castle door ready for her audience, which is expected to last for around 30 minutes before she departs at around 12.40pm.
The new PM’s departure, as is the custom, will be filmed.
Ellie Wilson, meteorologist at the Met Office, said: “It’s going to be a showery day as it has been today, especially in London, with a risk of thunderstorms particularly through the afternoon from midday onwards.
“That’s continuing all the way until late afternoon, early evening. There’s a chance of hail too.
“In Scotland, a little bit of a drier start but cloudy tomorrow morning. There’s a slow-moving front that’s going to move northwards through the late morning in the afternoon, which will bring some rain and drizzle over the hills. There’s also going to be some showers as well throughout the day in Scotland.
“In London, temperatures-wise, it’s going to be 24C to 25C, still feeling quite muggy.
“In Scotland, highs will reach 18C to 20C.”
— Met Office (@metoffice) September 5, 2022
Yellow thunderstorm weather warnings are in place on Tuesday for the west and parts of the south-west of England and across the east and south-east of Wales from 2pm until 2am.
The forecaster says residents could see flooding, damages to buildings and loss of power as they face spray, standing water, hail and gusty winds.
The yellow weather warning has also been issued from 8.35pm Monday to Tuesday at 6am across the south east and east of England.