Britain is due to quit the EU on Oct. 31, but has yet to agree a divorce settlement with Brussels.
Without a deal, EU regulators have said that EU-authorised investment firms can only trade shares listed in the bloc on platforms inside the EU, threatening London's central role in European share trading.
Aquis will offer trading in euro shares in Paris and London.
"We will be in a position to be able to trade for our customers in any place they wish to trade," Aquis Chief Executive Officer Alasdair Haynes told Reuters after Aquis reported latest earnings.
This, however, would mean that markets in euro shares would fragment, making it harder for investors to find the best deal, Haynes said. "Over a period of time, liquidity will move from one place to another."
Aquis first-half 2019 losses shrank to 160,000 pounds ($198,720.00) from 1.6 million pounds in the year ago period.
Haynes said he agreed with analysts who expect the exchange to be profitable in 2020. Its agreed acquisition of NEX Exchange, which Aquis will use to enter the listings market, is expected to obtain UK regulatory approval later this year.
Aquis accounts for 4.8% of European share trading, and Liberum analysts said on Tuesday they expect this to reach 10%. Haynes said that once Brexit uncertainty has ended, Aquis should flourish as investors return.
BREXIT FIRST MOVER
Aquis and rivals CBOE and Turquoise trade shares listed on national exchanges.
CBOE will offer trading in shares from all EU countries, apart from Britain, on its new Amsterdam platform on Oct. 1 regardless of what form Brexit takes later that month.
It means that European share trading will fragment, reversing years of efforts by the EU to create a seamless cross-border market that is cheaper and more efficient for investors to compete better with the United States for raising funds for companies to grow.
CBOE already accounts for about a fifth of share trading in EU shares, and Haynes said he was not worried that the U.S. rival will gain first mover advantage.
"I don't think any real trading is going to take place until there is a no-deal Brexit. The real test will be on November 1, post-Brexit in a no-deal scenario," Haynes said.
Turquoise has not announced the start of trading in the Dutch financial capital.
Share trading is not the only financial activity leaving London to nibble away at the capital's role as a global financial centre.
In March CME moved about 230 billion euros of daily trading in euro-denominated repurchase agreements and government debt from London to a new hub in Amsterdam, with clearing of those contracts shifted from London to Paris.
The London Stock Exchange has moved trading in euro zone government bonds from London to Milan.
But figures this week from the Bank for International Settlements showed that since Britain voted in 2016 to leave the EU, London has remained the world's biggest currency trading centre, and has overtaken New York to become the biggest centre for trading interest rate derivatives.
(Reporting by Huw Jones; editing by Emelia Sithole-Matarise)
By Huw Jones