Amsterdam ousted London as the largest financial trading centre in Europe last month as Brexit-related changes to finance rules came into force.
About €9.2bn (£8.1bn) worth of shares were traded on Amsterdam exchanges each day, against €8.6bn in London.
Following new Brexit rules, EU-based banks wanting to buy European shares currently cannot trade via London, meaning a loss of fees for City firms.
Bank of England chief Andrew Bailey has warned the EU not to cut off London.
On Wednesday, Mr Bailey said there were signs that the EU planned to cut the UK off from its financial markets.
Following the new Brexit trading rules coming into effect, there are talks to harmonise rules over financial regulations - so-called equivalence
Both sides are working towards a March deadline to agree an "equivalence" regime under which the UK and Europe would recognise the other's regulations.
Number 10, said it remained "open" to discussions with the EU on the equivalence issue.
"Despite the fact that we've supplied all of the necessary paperwork and are one of the world's most preeminent financial centres, with a strong regulatory system, the EU still haven't granted us full equivalence."
"This has meant that some meant a number of EU shares that were previously traded on UK venues, have moved to the EU venues on advice of the European regulator, but our position is fragmentation of share trading across financial centres is in no one's interest," it added.
It's called invisible trade - but selling services abroad is something the UK excels in, particularly when it comes to banking.
Financial services makes up about 7% of the UK's income in total, and about 40% of banking and investment's business abroad is with the EU.
But its needs were largely invisible from the deal struck with the EU at the end of last year. The diversion of share trading is the first visible, if inevitable, sign of the impact.
And that business may not return to London. Even if the UK government and Brussels can ultimately reach agreement that financial services can get more access to each others markets, on the basis the UK's standards can be deemed "equivalent" to the EU's, share dealing may not be part of that.
The UK government hopes Brexit will enhance the City's dominance, with scope to deepen relationships with other financial centres. But that's a work in progress.
The boss of one share exchange described a recently-struck deal that allows Swiss shares to be traded in London as being like a free kick in a football match rather than an equaliser: it doesn't compensate for what has been lost in loosening ties with Europe.