Australia, Israel, Sweden, Russia and Switzerland have all dumped coins, while even countries that use the euro - such as Ireland and Belgium - have introduced rounding so people don't get 1c and 2c in their change.
It has raised the prospect of scrapping the denominations in documents released as part of the spring statement.
The government paper - Cash and Digital Payments in the New Economy - questions whether the current mix of eight coins and four banknotes meets modern needs.
Despite seeking views on the future of cash, the Treasury says that coins still have a vital future in the UK.
Having excess numbers of both types of cash "does not contribute to an efficient or cost effective cash cycle", the paper adds, also pointing to the need to keep "confidence in the currency".
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The document adds: 'The cost of industry processing and distributing low denomination coins is the same as for high denomination coins, making the cost high relative to face value and utility'.
Ministers are also considering dropping the £50 note and implementing a limit on cash transactions that could make it illegal to pay builders cash in hand.
The Treasury said surveys showed 11 percent of those aged 25-34 said they "rarely used cash" at all, compared with only two percent of those aged 55-64.
"There is also a perception among some that £50 notes are used for money laundering, hidden economy activity, and tax evasion".
The decreasing use of cash for small-value transactions, together with the public returning stores of small change to banks, meant the issues were becoming more pronounced.
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The Treasury published a "call for evidence" on the proposed changes on Tuesday, saying that now most small denomination coins are only used once before being put in piggy banks or thrown away.
Sarah Coles, personal finance analyst at financial provider Hargreaves Lansdown, comments: "The writing looks to be on the wall for 1ps and 2ps".
"The Government welcome all contributions to the debate and will respond fully after the call for evidence closes on the 6 June".
The penny has been around since the 8th century, but the current decimal coins only came into circulation in 1971.
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