If temperatures reach that level it will be the hottest in 40 years, according to Sky weather presenter Jo Edwards.
The May Bank Holiday was introduced in 1978 and the temperature has never topped 28C.
Bank Holiday Monday in 1999 was 23.6C, while the hottest Bank Holiday weekend ever was in 1995 when temperatures peaked on the Saturday at 28.6C.
“We’ve got two records to break this Bank Holiday weekend,” said Edwards.
“The first, for hottest spring Bank Holiday Monday, is almost a dead cert now! The figure to beat is 23.6C (74.5F) while the figure forecast for the day is 27C (80.6F).
“In fact, there’s a 30% chance of some sheltered spots actually registering 28C (82.4F) or 29C (84.2F) on Monday which would be a very firm victory.”
She says high pressure is keeping the weather calm and settled at the moment, adding: “It would have to be a truly freakish turn of nature that would cool things down now.
“The second record would be that of ‘hottest ever Spring bank holiday weekend’ and this one might be a little harder to achieve.
“The figure we’d be chasing here would be 28.6C (83.5F) so we’ve got about a 30% chance of equalling an old record or setting a new one. These temperatures are 8C or 9C above what we’d expect at this time of year so it shouldn’t be too disappointing if it cools down a little in the week to come.
“Fortunately there’s still a lot of sunshine in the forecast.”
Sunday saw highs of 26C in Heathrow, and Scotland and Northern Ireland had their hottest day of the year so far, with Edinburgh recording temperatures of 22.3C and Katesbridge 21C.
Met Office forecaster Craig Snell said: “It looks likely we’ll at least see our warmest Bank Holiday Monday on record on Monday.”
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The record highest temperature for May is 32.8C (91F) which was recorded in 1922 and 1944.
Bookmaker Coral has cut the odds on this month seeing the hottest May day ever recorded to 6-4 from 2-1.