In the event of a Brexit, the company "would move quickly to create a legal and regulatory framework" to assure investors they can carry on trading, Mark Hemsley, chief executive officer of Bats Europe, told Reuters.

"A Brexit would create a situation where it is much harder to trade out of London into Europe and likewise for European customers to want to trade via London," Hemsley said.

"Investors need to know that they can carry on trading."

The CEO of Deutsche Boerse (>> Deutsche Boerse AG), which is pursuing a $30 billion (£20 billion) merger with regional rival London Stock Exchange (>> London Stock Exchange Group Plc), said last month that Frankfurt could benefit as a financial centre from a British vote to leave the EU.

The Brexit campaign seems to have gained momentum over the Remain camp in the past week, two online polls suggested on Monday, though the City of London financial community is overwhelmingly in favour of Britain staying in the EU.

Bookmakers shortened their odds on Brexit in response, with betting website Betfair putting the chances of a vote to leave at 30 percent on Monday. The odds were at around 27 percent at the start of last week.

Brexit was mentioned as a risk factor in a filing Bats Global Markets made with the U.S. Securities and Exchange Commission in January before the firm's initial public offering. A date for the referendum was not known at the time.

A Brexit, on which Britons will vote on June 23, would probably be negative for overall equity market volumes, Hemsley told Reuters. "However it may well increase forex activity."

Overall equity trading volumes in Europe have fallen by nearly a third so far in 2016 compared with last year as sluggish earnings, political uncertainties and a trendless market have kept investors on the backfoot.

European shares are down 2.7 percent, in U.S. dollar terms, lagging broader developed as well as emerging markets indices this year.

Bats Europe has maintained its position as the top regional stock exchange through 2016 with a roughly 20 percent share of total equity trading, according to Thomson Reuters Market Share Reporter.

(Reporting by Atul Prakash; Editing by Mark Heinrich)

By Atul Prakash