Ministers are considering putting extra conditions on banking licences after a row over the closure of Brexiteer Nigel Farage's account at Coutts.
It follows reports that lenders could lose their permits if they cut ties with customers because they disagree with their political views.
Mr Farage has accused Coutts of lying about its decision, saying he was "cancelled" by the bank.
Coutts says decisions to close an account "are not taken lightly".
Government sources told the BBC that the possibility of putting conditions on banking permits was being explored, although no decision had been made.
Banks would also be required to explain why an account is being shut, and give a longer notice period, under tougher rules to be brought in.
According to the Times newspaper, licences could be stripped in order to protect customers' right to free speech.
The BBC understands that the Treasury is also seeking clarity on the handling of Mr Farage's accounts from Alison Rose, the boss of NatWest, which owns Coutts.
It comes after Mr Farage obtained documents, which have been shared with the Mail newspaper, from minutes of a Coutts meeting where both "commercial" reasons and "reputational risk" associated with his political views are cited as reasons behind terminating his account with them.
The 40-page report, obtained under a Freedom of Information request, mentioned Brexit and his alleged links to Russia.
Banks do have the right to what's known as "commercial independence" to make decisions about their company, and who their clients are.
For example, Coutts very openly advertises that it excludes anyone who is not a millionaire.
'Uncomfortable'
Angela Knight, former chief executive of the British Bankers' Association, told the BBC's Today programme that banks were not allowed to have certain people as customers, but that there was a grey area around so called "political exposed persons" such as Mr Farage.
She added: "I do find it somewhat uncomfortable to see a situation arise where because of somebody's legitimate views, even though you don't agree with them, it somehow has resulted in a service being withdrawn and they are not being told about it."
She added: "In this instance what seems to have happened is nothing was really said to the individual concerned and then when they put in an application under the Freedom of Information Act, they suddenly find that there's a whole series of reasons which seems to centre around what they have said."
On Thursday the former UK Independence Party leader welcomed reports of a government crackdown, saying closing bank accounts for political reasons could stop people from going into public life.
"Refusal to open [accounts] and closures have happened to several members of my family... Which is perhaps, above all, what has made me angry, really angry and motivated me to [speak out]."
'Shocked'
It came after Prime Minister Rishi Sunak tweeted that shutting someone's account over their views was "wrong", calling free speech the "cornerstone of our democracy".
Meanwhile, Home Secretary Suella Braverman said elsewhere that the Coutts row "exposes the sinister nature of much of the diversity, equity and inclusion industry".
The BBC had previously reported Mr Farage had fallen below the financial threshold needed for an account at Coutts, citing a source familiar with the move.
The former politician accused the broadcaster of falling for "spin" and restated that he had been targeted for his political views.
He cited the report by the bank's reputational risk committee which states that the Brexiteer's views did not "align with our values".
"Apparently, I'm a risk to them. I have virtually no links of any kind to Russia whatsoever. This is political. There is no other way of looking at it," he said.
He later told BBC Newsnight he was "literally shocked" when he saw the report, which he described as a "personal hit job". "This bank is behaving now like a political campaigning organisation," he said.
But economist Frances Coppola told the same programme that "having read the report, I actually don't think that's the reason why they closed his account. The report makes it clear that the reason they closed the account was that Nigel paid off his mortgage and the house was released as a security and that brought him below the criteria for an account at that bank."
Coutts has said it has offered Mr Farage an alternative account at its sister bank, NatWest and the offer still stands.
Anyone concerned that they have not been treated fairly by their bank can appeal to the Financial Ombudsman Service.
City regulator the Financial Conduct Authority is also talking to NatWest about the handling of Mr Farage's accounts, its boss told MPs on Wednesday.
Nikhil Rathi said that current rules made clear banks should not discriminate on the basis of political views.
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