Workers should be allowed to dress more casually, as temperatures reach record levels, the TUC has said.
The heatwave will hit most of the country this week
It believes air conditioning could be turned down or even turned off if there was a more relaxed dress code.
It was the hottest day of the year on Monday with 32.7C (90.9F) recorded at Heathrow Airport in London.
The BBC Weather Centre said it expected London temperatures to reach 37C (99F) on Wednesday, beating the July record of 36C (97F) in Epsom, Surrey, in 1911.
The heat has brought problems to residents in York, where 500 homes have been left without water after a series of mains burst across the city on Tuesday.
Yorkshire Water said a power surge had caused at least 10 mains fractures across the city.
Forecasters say Yorkshire and Humber is expected to experience its hottest July weather in nearly two decades.
And the heatwave across England is set to continue on Tuesday, with temperatures expected to hit up to 34C (93F).
Rail lines buckled as a result of the heat in the Midlands on Monday, while glass panels fell at a Newcastle bus station.
Transport for London repeated its advice to passengers to carry water with them on the Underground.
Precautionary speed restrictions were in place on outdoor stretches of track on the District, Piccadilly, Metropolitan, Jubilee and Northern lines.
Organisers of The Open golf tournament, which starts at the Royal Liverpool course in Hoylake on Thursday, fear the weather could affect playing conditions, with greens needing to be watered if they get too dry
Thames Water, which supplies areas in and around London, said reservoir levels were at 100% capacity outside of the capital, but 90% within it.
A spokeswoman told BBC News: "Most of the storage capacity that we use is actually underground, where levels are currently below average."
A spokeswoman for Severn Trent Water, which supplies Midland areas including mid-Wales and the East Midlands, told BBC News: "While reservoir levels remain high at around 80%, water consumption during last week's hot spell increased by 200 million litres per day.
"This is the equivalent of supplying an extra 800,000 people every day."
BBC weather forecaster Tomasz Schafernaker said there was a "10% chance" the UK's all-time record of 38.5C (101F), recorded in August 2003, could even be beaten.
"On Tuesday and Wednesday, temperatures in the Midlands will rise to around 34C and 35C so already there will be some local records broken for July," he said.
He added that in Wales the forecast for Tuesday was for temperatures "well into the 30s" and that the border area and across to Birmingham could reach 37C (98F).
All-time UK temperature record is 38.5C (101F) set in August 2003
UK record for July is 36C (97F) set in Epsom, Surrey in 1911
London temperatures expected to reach 37C (99F) on Wednesday
Previous hottest day of 2006 was 12 June, with temperature of 32.4C (90F)
But forecasters say there is a chance of thunderstorms in Wales tomorrow and that the Welsh record of 35.2C (95F) set at Hawarden, Flintshire, in August 1990, could be broken in the south-east region on Wednesday.
In Scotland there is slight drizzle on the coastlines and in the north, but inland the temperatures should reach about 29C (84F) and remain into Wednesday.
In Northern Ireland Tuesday is another fine and sunny day in all areas, but will be particularly hot in western counties.
A sea breeze is keeping eastern coastal areas and Belfast cooler than Monday, and the Met Office said the outlook for Wednesday was fine, sunny and very hot.
The TUC said employers should follow Japanese Prime Minister Junichiro Koizumi, who urged his country not to wear jackets and ties during summer.
TUC general secretary Brendan Barber said: "Not only will a cool approach to work avoid staff wilting at their desks, it could also save companies money as they should be able to turn down the air con a notch.
"Arctic-style air conditioning may stop the workplace from becoming like an oven, but its overuse is not good for the environment.
"It's no fun working in a baking office or factory and employers should do all they can to take the temperature down."
Meanwhile, the Restoration of Appearance and Function Trust, which includes experts in sunburn, has argued that rubbing suncream into the skin does not offer the best protection from the sun.
It says letting a white film dry on is much better.
Cancer Research UK recommended people should stay out of the sun between 11am and 3pm, adding that suncream should be the last line of defence against the sun's rays, not the first.