Temperatures could soar to more than 34C (93.2F) in some parts of the country on Wednesday, beating the 33C (91.4F) recorded at Porthmadog in North Wales on June 28.
Met Office forecaster Alex Burkill said: "It does look likely it will be at least 33C at some point this week, most likely on Wednesday or Thursday, in the south east and east, London, Essex, Kent, east Anglia and into Lincolnshire - and that would make it the hottest day we have had so far."
Temperatures are likely to be lower elsewhere.
Forecasters said there is a chance of hitting 34C or 35C (95F), which could put Britons in line for the hottest day since the mercury hit 34.5C (94.1F) at Heathrow on June 21 last year.
The hottest July day on record is 36.7C (98F), which was reached at Heathrow on July 1 2015.
The hot weather will lead to thunderstorms and it "could all happen on the same day", Mr Burkill added.
He said: "The heat and humidity means there is a lot of energy in the air and a high risk of intense thunderstorms. Whether or not it will happen is where the uncertainty is."
Nearly all parts of the UK are seeing above average temperatures, but it will be hot or very hot towards the east or south east.
During the current heatwave, UK temperatures have been approximately 10C higher than average for this time of year.
Instead of 23C (73.4F) which could usually be expected in London in July, temperatures could tip 34C (93.2).
Scotland, which averages 17C (62.6), could enjoy highs of up to 25C (77F), while Wales could jump to 26C (78.8F) or 27C (80.6F) instead of 19.2C (66.5F).
Those in Northern Ireland may be basking in 24C (75.2F) rather than the July average of 18.5C (65.3F).
Mr Burkill also said the current run of fine weather looks set to continue.
He said: "It always seems that when the schools break up that is when we get the bad weather, but in this instance that is not the case."