However, temperatures could fall to as low as 11C in the capital by the end of next week as the weather cools.
The Met Office forecasts some level of rain in London every day after until at least next Friday.
London is set for a rainy spell
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Showers are expected to be “most frequent and heaviest” in northern and western areas of the country on Sunday.
June is set to begin with rain showers seen more widely, broken up by some “brighter intervals”, forecasters said.
Met Office meteorologist Greg Dewhurst said next week will bring “a change from the heatwave” as temperatures fall closer to average.
He said: “It’s been quite a dry period of weather and hot period of weather, so it will be probably much needed and much welcome rain to gardeners and growers and farmers with the ground being so dry at the moment.
“So it is a change, but probably a welcome change for those who either don’t like the heat or want some rain.”
Mr Dewhurst added that there are “good signs” the heat will return, with warm spells likely following an “unsettled” start to June.
He said: “Particularly (during) the middle to second half of June, it looks like it starts settling down with higher pressure a bit more dominant again, so an unsettled start to meteorological summer, but there are signs that it does settle down as the month goes on.”
It comes after England and Wales recorded the hottest days in May on record on Tuesday.
Charlie Noble, 16, became the 12th person to die in a water-related incident over the course of the heatwave when his body was recovered in Stirlingshire, Scotland, on Thursday.
There have been deaths in South Yorkshire, West Yorkshire, Cornwall, Hampshire, Warwickshire, Cheshire, Pembrokeshire, Lincolnshire and Lancashire.
Thousands of people in Kent are expected to face water issues this weekend as South East Water continues to grapple with its supply during the hot weather.
Businesses have closed and residents have been queuing up at water bottle stations since problems began amid the bank holiday weekend heat.
