If accurate, Britain will be hotter than Portugal, Jamaica, Costa Rica, the Canary Islands and Cyprus.
It would also mean the hottest day of the year so far, eclipsing the record of 27.5C (81.5F) set in mid-May at Heathrow.
“We should beat that comfortably on Friday and potentially exceed it, or get very close to it, on Wednesday and Thursday as well,” Mr Keates said.
The meteorologist added that heatwaves – three consecutive days of high temperatures – were possible between June and mid-September.
“We think at the moment it will be warmer than average with an increasing likelihood of heatwaves,” he said.
“There have been no heatwaves so far this year. The greater likelihood is that it’s going to be the further south or south-east you are.”