The forecaster has issued a level three heat warning from Thursday morning as it expects hot air to move in from southern Europe, leading to a sudden increase in temperatures.
Britain is expected to pass the threshold for a heatwave, which requires three consecutive days of temperatures over 25C across most of the country, and 28C in London.
The mercury is even expected to soar to 37C by Friday in the south east - meaning London would be hotter than sun-drenched Caribbean holiday destinations.
It is possible Friday will even see the capital surpass the 37.8C (100.04F) recorded in Heathrow on July 31 – the hottest day of the year so far, and the UK's third warmest day on record.
Met Office forecaster, Oli Claydon, said: "There's a strong likelihood London and the south east could see a heatwave this week, with four or even five consecutive days of incredibly warm temperatures reaching a high of 37C on Friday.
"It is the result of southerly winds moving from Europe and parts of northern Africa, which will push the temperatures up."
Thursday is expected to begin overcast for most of the country, but will be a dry day for all, with the sun appearing through the clouds by the afternoon and temperatures pushing to 30C in the capital.
Wales and the north and south-west of England will be sunny, with temperatures reaching around 25C, although Scotland is set to see rain and highs of 22C.
Mr Claydon added: "Saturday will likely be another hot day for southern and central parts of the UK, with heatwave conditions potentially continuing in parts of southern and south-east England.
"Sunday should be the last of the heatwave conditions, before cold air moves in overnight leading to some thundery showers on Monday."
The Met Office has already urged people to be careful this week, as UV levels will be higher in the sunshine.
Deputy chief meteorologist David Oliver said: “High temperatures could trigger some thunderstorms across southern parts of the UK over the weekend, but for most there will be plenty of dry and sunny weather.
"At the moment there is some uncertainty as to how long the hot spell of weather will last".
A Met Office report on Wednesday suggested that the period of beautiful weather could come to a swift end next week.
It warned that "confidence remains fairly low for the last two weeks of August and into early September" in terms of dry, sunny weather.
The report said the UK is likely to see dry spells "interspersed with occasional bouts of wetter and windier weather" as the summer ends.