Britain introduced a "temporary permissions regime" or TPR to allow EU companies to continue operating in Britain after Brexit, giving them time to apply for permanent authorisation.
When Britain was an EU member, EU firms could use the bloc's "passporting" system to sell their financial services in Britain from their European base without taking out a UK licence.
The Financial Conduct Authority said on Tuesday that European firms wishing to remain in the TPR while they await a "landing slot" or date for permanent authorisation need to meet the FCA's standards.
"Firms may be asked to stop undertaking new business or could be removed from the TPR if they miss their 'landing slot', fail to respond to mandatory information requests, have no intention in applying for full authorisation, or if their authorisation application is refused," the FCA said in a statement.
The watchdog said it had already cancelled the temporary permission of four firms who failed to respond to mandatory information requests.
"We expect firms operating under the regime to be responsive to our requests for information, and that are coherent in their business planning," said Emily Shepperd, the FCA's executive director for authorisations. "We will continue to act against firms that fail to meet our standards."
EU firms have to weigh up whether there is enough business in Britain to warrant the expense of obtaining a licence.
The FCA has said that 995 of the 1,361 firms in the TPR are expected to apply for authorisation, with 366 not expected to apply.
(Reporting by Huw Jones. Editing by Jane Merriman)
By Huw Jones