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Rather than go to the bank in person, customers will be able to photograph the cheque, and send it electronically.
The government is to launch a consultation on the idea, with a view to making the necessary legal changes.
The technology will also allow cheques to be cleared in two days, rather than the six it takes at the moment.
Banks say the new transfer method will be more convenient, and more secure.
"Moving into a virtual world will actually create a more secure customer experience than the paper experience today," said Antony Jenkins, the chief executive of Barclays.
Such photos would not be stored on the phone itself, so there should be no security risk if a phone was stolen.
Similar technology was introduced in the United States nine years ago, following the attack on the World Trade Centre.
A new law known as Check 21 was passed, to enable banks to process cheques electronically, rather than having to transport paper versions across the country.
The government believes a change in the law in the UK would also promote the continuing use of cheques.
The UK Payments Council was originally planning to abolish all cheque payments by 2018, but was forced to change its mind after public opposition.
"We want to see more innovation so that customers see the benefits of new technologies," said Sajid Javid, the financial secretary to the Treasury.
"We want cheques to have a crucial role in the ongoing success of the UK," he added.
In 2012, 10% of all payments by individuals were made by cheque, and 25% of payments by businesses.
The industry says most younger account-holders already use electronic systems of payment, and rarely use cheques.
However all customers will still be able to pay in cheques by posting them to their bank, or by visiting their bank directly.
Barclays is planning to launch a pilot programme for paying in cheques via phone from April 2014.
It hopes to launch a service for all its customers later in the year.
But the new technology is likely to raise further questions about the size of the branch network, as customers turn to banking via PCs and mobiles.
Last month Barclays announced 1700 further job losses in its High Street branches, as a direct result of mobile technology.
In the year to July 2013 it closed 37 branches, and it has hinted at more closures to come.
"I think people are going into branches less and less, particularly as a result of mobile banking, and that's going to accelerate the process," Antony Jenkins told the BBC.
The bank is in the process of moving eight of its branches into stores operated by Asda.
A spokesman said customers would always be able to pay their cheques in at a branch if they wanted to.