If the UK exits the EU without an agreement there is likely to be an impact on the liquidity of the stock market, according to the Financial Conduct Authority (FCA).
The EU has published Share Trading Obligations (STO) to address the issue and this will help ensure that UK listed shares of companies with their primary stock market listing in the UK will be able to be traded with little disruption.
But the regulator warned that companies that have shares listed in both the UK and an EU country, could see "disruption to investors, some issuers and other market participants, leading to fragmentation of markets and liquidity in both the EU and UK".
The regulator called on the EU to adopt "equivalency" for a short period in the event of a no deal, as a way to mitigate these risks.
Equivalency means treating the UK regulations as equal to those of the EU for a fixed period of time until the disruption is eased.
The regulator said: "The FCA believes in open markets and competition between trading venues and that reciprocal equivalence - which reflects the reality - remains the best way of dealing with overlapping share trading obligations.
"The UK has onshored the same regime, making us one of the most equivalent countries in the world.
"In the absence of reciprocal equivalence, applying both UK and EU STOs in a way that maintains the status quo for a limited period of time after exit remains an alternative way of mitigating disruption whilst longer term solutions are found.
"The FCA stands ready to use the extra time available due to the delay to the UK’s withdrawal to engage constructively with ESMA and other European authorities to achieve either of these outcomes."