Video report by ITV News Correspondent Lucy Watson
The body of a man was pulled from the River Thames at around 4.30pm on Wednesday, Scotland Yard said.
A search with police divers was launched after a 47-year-old reportedly entered the water in Kingston, south west London, and began swimming on Tuesday evening.
It comes after a body was recovered on Wednesday morning.
He is believed to be a 23-year-old man who vanished while swimming in the Thames at Shadwell Basin on Tuesday.
Separately, a body was found on Tuesday evening in the search for a man in his 20s from Wiltshire, who went missing in the lake at Cotswold Water Park, Gloucestershire Constabulary said.
The UK is bracing itself for what could be its hottest ever day on Thursday.
According to the Met Office, there is a 70% chance the mercury could rise above the current all-time temperature record of 38.5C on Thursday.
Conditions could reach 39C in southern and eastern England, it tweeted.
Emergency services have warned the public to take precautions during the extreme heat and highlighted the risks of cooling off in the sea, lakes and rivers.
Inspector Stuart Simpson, from the Metropolitan Police’s Marine Policing Unit, said: “Whilst at times, the Thames may look appealing, especially in this hot weather, it remains very dangerous all year round.
“On initial entry, the water can seem warm on the surface, but further in it can be freezing cold and there are often very strong undercurrents.
“The initial shock of the cold water is often what leads to people going subsurface and subsequently drowning.”
With temperatures topping 30C in the South East on Wednesday, Network Rail has warned train speed restrictions may be introduced in areas where tracks are at risk of buckling.
Extreme weather action teams (EWATs) have been “activated” to keep passengers safe and trains running, Network Rail said.
The Rail Delivery Group, which represents the industry, advised passengers in London and the South East to consider changing their travel plans on Thursday because of the expected heat.
Robert Nisbet said on behalf of train operators and Network Rail: “This week could see record-breaking hot weather for Britain.
“While train operators and Network Rail are working together to minimise disruption, we ask passengers to check before they travel and consider travelling earlier on Thursday if possible.
“We also ask people travelling by train to carry a water bottle and if they feel unwell, get off at the next stop where a member of staff will be happy to help.”
The Met Office issued a yellow warning for scattered thunderstorms covering the east of the country from Scotland down to London from 3pm on Thursday and into early Friday.
It warned that flooding and lightning strikes could affect driving conditions, disrupt train services and lead to power cuts.