Many London-based businesses had prepared for the new conditions by setting up units in the EU, and Monday put those new arrangements to the test.
Trading on Cboe Europe and London Stock Exchange's Turquoise units in Amsterdam, and on Aquis Exchange's new Paris platform, grew steadily on Monday morning, with no glitches reported.
Data from Cboe, Europe's biggest cross-border share trading platform, showed that two hours after the open, 60% of all of its activity was at its Amsterdam unit.
"All our systems are operating normally, and as expected the majority of activity in EEA-symbols (mainly EU listed shares) is now taking place on our Dutch venue, with activity across all our market segments," Cboe Europe president David Howson said.
"We will continue to work with clients to ensure a smooth transition over the coming days and weeks."
Aquis reported a "clean shift" in euro share trading from its London base to its new Paris unit, with the French capital now the location for most of the group's business.
Trading on Turquoise was roughly split between London and Amsterdam.
No European trading of note had taken place on the three EU hubs until Monday.
Trading in non-EU listed shares remains in London.
"I don't think there has been any impact from this switch," said Keith Temperton, equity sales trader at Forte Securities. "It has been planned for years."
Britain's Financial Conduct Authority (FCA) and the EU's European Securities and Markets Authority (ESMA) had no comment.
Banks and other financial market participants in the EU are also required to trade swaps, a type of derivatives contract, on platforms inside the bloc and stop using venues in London, the world's biggest centre for trading swaps.
In a last minute intervention on Dec. 24 before markets shut until Monday, the FCA said it would allow UK market participants to trade swaps on EU venues until the end of March to avoid disruption in markets.
Traders said that on Dec. 24 the spread between the 10-year interest rate swap EURIRS on Deutsche Boerse's Eurex in Frankfurt and LSE's LCH swaps clearing unit in London ballooned by 35 basis points.
This signified that it was more expensive to use Eurex Clearing than LCH as customers clambered to move business from London to Frankfurt before markets closed on Dec. 31.
A trader said that normally there is little or no spread between the two clearing houses.
Christoph Rieger, head of rates and credit research at Commerzbank in Frankfurt, said there was no big disruption in initial trading on Monday.
"As far as I am aware, preparations by all the major players had been done already, they had done their homework and made their plans," Rieger said.
ESMA on Monday cancelled its authorisation for four trade repositories in London used for reporting derivatives trades, in a further sign of the British capital being locked out of EU markets.
(Additional reporting by Thyagaraju Adinarayan and Dhara Ranasinghe; Editing by Rachel Armstrong and Mark Potter) ((email@example.com; +44 207 542 3326; Reuters Messaging: firstname.lastname@example.org))