The regulator said it believes the firm is providing financial services or products in the UK without authorisation.
Almost all firms and individuals offering, promoting or selling financial services or products in the UK have to be authorised or registered by the FCA.
However, the City watchdog said Spring Well Bank, with an address in Thatcham, is targeting people in the UK.
It warned consumers to take caution as they will not have access to the Financial Ombudsman Service or be protected by the Financial Services Compensation Scheme (FSCS).
It said: “Be aware that some firms may give out other details or change their contact details over time to new email addresses, telephone numbers or physical addresses.”
According to the Spring Well Bank website, it offers the ability to open an account online, transfer money and invest it.
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