The crypto exchange said that stock tokens are unavailable for purchase on its website effective immediately.
The regulator said last month the unsupervised spread of crypto was a cause for concern.
World regulators have announced warnings around Binance, drawing attention to the exchange's operations and hinting at future actions.
The exchange's move reportedly came after Faster Payments ended its agreement with Binance.
The decision was taken after the FCA said Binance is not permitted to undertake any regulated activity in the U.K.
The bank said it’s heeding the FCA’s warnings about Binance.
Bitstamp has seen customer numbers more than double since the FCA said Binance Markets should not be operating in the U.K.
The crypto exchange is looking for a U.K.-based ex-regulator or government official, according to people familiar with the plans.
"We are seeing wider adoption of cryptocurrencies globally and the need for clearer regulatory frameworks in different countries," said CZ.
Manuel Alvarez ran California's Department of Financial Protection and Innovation.
The exchange has faced increasing headwinds in Europe over the past two weeks.
The bank is monitoring cryptocurrency activity and placing extra safeguards on certain activities.
An FCA warning refers to Binance Markets, not www.binance.com, the crypto exchange said.
Barclays appears to be contacting customers who have used their cards on Binance this year advising them that this is being stopped.
The SEC alleges the crypto exchange is operating a digital-asset business in the country without a license.