Video report by ITV News Correspondent Rupert Evelyn
Heathrow Airport was the hottest place in England, slightly ahead of Northolt in west London, which registered temperatures of 33.0C.
Trawsgoed near Aberystwyth was the warmest place in Wales, with a top temperature of 24.3C, while Fyvie Castle in Aberdeenshire, Scotland, saw highs of 24.0C.
In Northern Ireland, thermometers peaked at 21.2C in Killowen.
The previous record was 28.2C set at Holbeach in 2017.
The Met Office said the hot weather is expected to last for the rest of the day, although parts of the country could be in for storms and thunder later in the week.
Senior meteorologist Greg Dewhurst said: "We reached 28.6C at about 11am and it was 28.9C a short time later.
"But we will see changes as we go through the week, with the chance of some thunder and showers across the country from Tuesday.
"The south east of England will hold on to the sun for an extra day, and we could see temperatures in the low 30s."
Temperatures hit an August Bank Holiday high of 33.3C (92F) at Heathrow on Sunday, while hundreds of thousands of people enjoyed what is thought to be the hottest Notting Hill Carnival ever in west London.
The previous best late August Bank Holiday temperatures before this weekend were 31.5C (88.7F) at Heathrow in 2001, 27.3C in Velindre, Powys, in Wales and 27C (80.6F) in Knockareven, Co Fermanagh, both in 2003, plus the 26.7C (80.06F) that was recorded in Aviemore, Inverness-shire, in Scotland in 1984.
Wales enjoyed a record 28.6C in Hawarden on Sunday when the top temperature in Northern Ireland was 24.2C at Stormont Castle.
Scotland's top temperature was the 28.4C recorded at Bishopton near Glasgow on Sunday.
Monday is not a bank holiday in Scotland.
The late summer sunshine, as a result of warm air being dragged up over the UK from France, comes at the end of what has been a wet and chilly month so far.
The extreme weather prompted vets to issue a warning to dog owners about over-exercising their pets in high temperatures.
Pet emergency firm Vets Now said flat-faced breeds, such as French bulldogs and pugs, were particularly susceptible to overheating.