Prime Minister Rishi Sunak confirmed the planned ban was being pushed back five years from 2030 to 2035.
He said it was "not right to impose more costs on working people", adding "sensible green leadership" was needed.
Ford said the move undermined its electric car investment plans, but Toyota welcomed the announcement, saying the delay was "pragmatic".
The UK's motor industry body, the Society of Motor Manufactures and Traders (SMMT), raised concerns that the delay could put off drivers switching to electric vehicles.
What's the policy now?
Prior to Mr Sunak announcing a shift in policy, the government had planned to ban the sale of new, pure petrol and diesel vehicles by 2030. Now, the plan is the ban will begin in 2035.
By phasing out petrol and diesel sales it aims to accelerate the transition to electric vehicles and expand charging infrastructure and achieve net zero by 2050, is when a country's net carbon emissions are cut to zero, and is seen as vital to tackling climate change.
Under the ban, from 2035 only electric battery-powered cars and certain hybrids will be able to be bought new.
However, most people will not be impacted by the ban immediately, as the majority of drivers buy vehicles second hand and only sales of new petrol and diesel models would be affected - not existing ones.
Mr Sunak said he expected the majority of cars sold by the time the ban commences to be electric, but added "at least for now, it should be you, the consumer that makes that choice - not the government forcing you to do it".
The delay in the ban brings the UK into line with the European Union, which is also banning sales of new petrol and diesel cars by 2035.
'Clarity required'
Ford, one of the UK's most popular car brands, selling more than 126,000 vehicles in 2022, criticised the change, saying it would "undermine" the move to electric.
Ford's UK chair Lisa Brankin said the original 2030 target "is a vital catalyst to accelerate Ford into a cleaner future", adding the company had already invested £430m in upgrading its UK plants to produce electric cars.
"Our business needs three things from the UK government, ambition, commitment, and consistency. A relaxation of 2030 would undermine all three," she said in response to the BBC reporting the prime minister was considering weakening several green commitments, to save money.
Stellantis, which owns Vauxhall, Peugeot, Citroen and Fiat, said it was "committed to achieve 100% zero emission new car and van sales in the UK and Europe by 2030", regardless of any delay to the ban.
But it added, "clarity and reasonable anticipation are important".
Toyota said the government's announcement was "welcome" adding it recognised that "all low emission and affordable technologies can have a role to play in a pragmatic vehicle transition".
Jaguar Land Rover said the move was "pragmatic and brings the UK in line with other nations, which we welcome".
But Mike Hawes, chief executive of the SMMT, said consumers would be sent an "incredibly confusing" message due to the delay.
"The concern now is, does this cause consumers to delay their purchase [of an electric car]?," he told the Today programme.
Simon Williams, head of policy at the RAC motoring group, said the announcement of the delay risked "slowing down both the momentum the motor industry has built up in switching to electric".
Drivers campaign group Fair Fuel UK said it was "delighted" by the delay, arguing the policy costs outweighed the benefits and the original plan was "always doomed to be dropped".
Philip Nothard, insight and strategy director at Cox Automotive, said many car makers were already committed to hybrid and electric-only ranges ahead of 2030, so regardless of the delay consumers would end up facing a "limited choice" of new petrol and diesel cars, which would likely be more expensive that greener cars.
But there have been concerns about the high cost of many electric vehicles, along with fears the UK is not expanding its charging infrastructure fast enough.
Mechanic Chloe Hudson told BBC Newsbeat that while a ban was good for the climate, the cost of living also played a part, and spare parts for hybrid and electric cars were expensive and unaffordable to some people.
"When something goes wrong, is that person then prepared to spend thousands of pounds on their vehicle?" said the 25-year-old from Birmingham
In recent months, UK car industry and government has been ramping up investment in zero-emission cars.
Earlier this month, German car giant BMW announced plans to invest hundreds of millions of pounds to prepare its Mini factory in Oxford to build a new generation of electric cars, while Jaguar Land Rover-owner Tata confirmed plans in July to build a £4bn battery plant in Somerset.
The projects have been backed with government subsidies.
BMW sources said moving ban to 2035 would not change its plans and rubbished reports suggesting the government had promised to keep the 2030 target as a condition for its recent investment.
Separately, the SMMT's Mr Hawes said he was "assured" that the zero emission vehicles mandate, a requirement that 22% of cars sold by each manufacturer will be zero emission from 2024, would still be introduced.