Following the conflict between Nigel Farage and NatWest, the Treasury has scheduled a meeting with bank executives to discuss account closures.
Minister Andrew Griffith said there was "significant concern" over claims accounts are shut due to people's political views.
Dame Alison Rose, the CEO of NatWest, has expressed regret to Mr. Farage, who has demanded that she be questioned by lawmakers.
He says his account at Coutts, owned by NatWest, was shut because of his views.
The government was already looking into concerns that some people had their accounts closed or suspended due to their publicly stated views, but the row involving the former Ukip leader has focused public attention on the allegations.
In a letter to banks seen by the BBC, City Minister Andrew Griffith said the recent allegations of "client de-banking" had "raised significant concern in both Houses of Parliament".
He said the government will "take the action necessary" to protect lawful freedom of expression.
The BBC understands Mr Griffith's letter will be sent to 19 banks and financial services firms on Monday.
He said he would call for a discussion with bank bosses "at the earliest opportunity".
The latest government response comes after the Treasury announced plans to subject UK banks to stricter rules over closing customer accounts.
Banks will have to explain why they are closing accounts, and they will have to give a notice period of 90 days before closing an account, to allow people more time to appeal against the decision.
The new rules are likely to be brought in after the summer, the BBC understands.
When Coutts decided to close Mr Farage's account, he said it did not give him a reason.
Mr Farage subsequently obtained a document looking at his suitability as a Coutts customer.
It said that to have Mr Farage as a customer was not consistent with Coutts' "position as an inclusive organisation" given his "publicly stated views".
The document flagged concerns that he was "xenophobic and racist", and also raised concerns about the reputational risk of having Mr Farage as a client.
The boss of NatWest Group, Dame Alison Rose, then apologised to Mr Farage for what she called the "deeply inappropriate" comments.
She also said that she was commissioning a full review of Coutts' processes on bank account closures.
