Sir Jon Cunliffe said Britain should "continue to bring these activities and entities within regulation", including "most obviously, the need to protect consumers".
Offshore digital coin exchange FTX, which just weeks ago had been valued at $32bn (£27bn), collapsed earlier this month leaving one million creditors out of pocket amid allegations it had mishandled customer deposits.
The Bahamas-based cryptocurrency exchange, run by 30-year-old Democrat donor Sam Bankman-Fried, had an $8bn black hole in its budget when it filed for bankruptcy two weeks ago.
The failure of FTX has spread panic through global cryptocurrency markets, wiping roughly $100bn from the value of all digital assets in the past 10 days according to data from Coinmarketcap, as a web of 130 companies linked to the bust exchange were placed into bankruptcy.
Dozens of cryptocurrency companies and investors have found their assets caught up in FTX’s collapse.
On Monday, shares in publicly listed Grayscale, the world's largest cryptocurrency fund designed to track the price of bitcoin, were trading at a 45pc discount to the digital currency, falling a further 5pc in New York. Grayscale owns $10.5bn in bitcoin, but its value has plunged to $5.5bn.
Grayscale on Friday refused to share proof of its cryptocurrency reserves, blaming "security concerns". Cryptocurrency companies have been rushing to publish audits of their reserves in an effort to quell investor fears they are exposed to FTX.