In England, it is likely that a new UK record temperature could be set with an unprecedented red alert issued.
According to the Met Office there is a 50 per cent chance of temperatures reaching 40C somewhere in the UK.
Last year, there were two short periods of heatwave in the UK which were cooler than the temperatures forecast next week and more than 1,600 excess deaths were recorded in the UK, a senior health source said.
The source said that they “expect” to see excess deaths but that these are “avoidable” if people take simple action to keep cool.
Meanwhile, Scottish Water has drafted in road tankers to begin delivering supplies to parts of the country, such as the isle of Arran, beginning to show the first signs of drought. It has advised people to reduce unnecessary water use - especially in the garden.
A Scottish Government Resilience (SGoRR) meeting has also been held to prepare for the potential impacts, and issued advice including to “avoid excess alcohol”.
From Sunday the weather in Scotland will be sunny and hot, peaking on Tuesday, when the mercury will hover around 30C.
The amber warning indicates there may be some adverse health effects for people vulnerable to extreme heat, such as young children and the elderly, with the public warned to watch out for sunburn or heat exhaustion.
There is a possible risk of power cuts due to failures in heat-sensitive systems and equipment, and with more people likely to visit coastal areas, lakes and rivers, there could be an increased risk of incidents near water.
Justice Secretary Keith Brown, lead Minister for resilience, said: “Our resilience arrangements have been activated and stand ready at all times to coordinate a response to severe weather issues where required. We will continue to closely monitor developments.
“When temperatures increase, it’s important to monitor forecasts and follow public health advice, including staying hydrated and drinking plenty of fluids and avoiding excess alcohol.
“I would also urge people to look out for vulnerable family, friends and neighbours, as older people, those with underlying conditions and those living alone may struggle to keep cool and hydrated.
“Water safety incidents and drownings increase in hot weather and people should be aware of the dangers and use supervised beaches and pools when possible.”
The Met Office amber warning covers southern parts of Scotland including eastern parts of Dumfries and Galloway, much of the Scottish Borders and parts of East Ayrshire, South Lanarkshire and Midlothian. While these areas will see more extreme temperatures, it is likely that there will be high temperatures across much of the country, especially up the east coast to the Moray Firth.
The Scottish Environment Protection Agency (Sepa) has issued a water scarcity warning.
In the east, areas such as the Dee, Firth of Forth, Almond and Tyne catchment areas have been raised to moderate scarcity which means businesses that extract water from the areas should only do so “if absolutely necessary”, Sepa warned. This could impact businesses such as distilleries, farming and hydro-electricity.
The Clyde, Helmsdale, Earn and Spey catchments are now at alert level. The dry weather means river and groundwater levels across Scotland are low.
Nathan Crichlow-Watton, head of water and planning at Sepa, said: “The situation continues to deteriorate in the east of the country, with most areas now in alert or moderate scarcity level.
“We’re also now seeing conditions worsen in the south west and businesses that rely on water in this part of the country should also be thinking about how to be more efficient.
“Water scarcity is a very real threat as a result of climate change, and one which affects multiple industries across Scotland including agriculture, whisky production, golf and hydropower.”
There is no prospect yet of a hosepipe ban but Scottish Water said it was “closely monitoring" growing public water consumption, which 'could put pressure' on supplies.
Kes Juskowiak, water operations manager, said: “We will continue to monitor our reservoirs and other water sources closely. Continued warm weather, a lack of rainfall and continued high use levels in the home and garden could put pressure on supplies in the days and weeks ahead.
“We are doing all we can to maintain water supply to customers. That includes moving water around the network and where necessary bringing in additional supplies to communities via road tankers.
“I would ask that householders take a few simple steps to use water efficiently and use less wherever possible, but particularly in the garden.”
Train operators in England have warned passengers to avoid travelling early next week due to extreme heat, unless their journey is “absolutely necessary”.
In Scotland, ScotRail has also warned that services could be affected.
It said in a statement: "Rails can be up to 20C higher than the air temperature in hot weather, meaning they can expand or even buckle.
"For safety, we may need to run some trains at reduced speeds on these days."
The AA has warned that cars could feel like “mobile microwaves” and urged motorists to prepare for hot journeys by packing snacks, medication and water, and ensure pets and children are not left in passenger seats.
Drivers should also check their vehicle’s cooling system with a mechanic, particularly owners of older cars, according to the AA.
In England, the UK Health Security Agency increased its heat health warning from level three to level four – a “national emergency”.
Level four is reached “when a heatwave is so severe and/or prolonged that its effects extend outside the health and social care system… at this level, illness and death may occur among the fit and healthy, and not just in high-risk groups,” it said.
The Met Office red warning, for Monday and Tuesday, covers an area from London up to Manchester, and up to the Vale of York.
Met Office spokesman Grahame Madge said that temperatures reaching 40C would be a “historic event”.
“If we get to 40C that’s a very iconic threshold and shows that climate change is with us now,” he said.
“This is made much more likely because of climate change.”
Mike Childs, head of science, policy and research at Friends of the Earth, added: “Each year, the effects of climate breakdown are becoming more evident and more severe.
“Without meaningful Government intervention, millions of Brits, particularly older people and young children, will be at increasing risk from health-threatening heatwaves like the one we’re experiencing.”