Nearly 800 people have been detained at Northern Ireland ports for immigration offences in the space of a year.
And the overall total has soared by two-thirds, statistics have revealed.
The exact figure of people detained at ports including Belfast, Londonderry, Larne and Warrenpoint in 2015/16 was 775 - a rise of 66% on the previous year.
They included 73 criminals who had previously been deported from the UK and 30 foreign nationals with serious criminal convictions in the UK or abroad.
But a senior PSNI chief has said there is no specific reason for the increase, such as Brexit. He was responding to concerns by the former chair of the Assembly's Justice Committee, Paul Frew, who asked whether specific trends have emerged.
PSNI Detective Chief Superintendent Hugh Hume, however, said: "None of the arrests or detentions are necessarily directly linked to Brexit.
"It tends to be a number of people from outside the European Union who are detained and people who have been deported from the United Kingdom and are attempting to regain entry.
"We are not seeing any particular trends apart from the general upward movement.
"There is an uplift; that is certainly true. The Irish ports have come under some greater notice, perhaps, from some people, but I would not say there is a trend or any exploitation of Brexit specifically; it is not driving it per se."
The senior police officer also warned, however, that tariffs or immigration differences introduced as a result of Brexit could cause an increase in cross-border smuggling.
The warning was a reply to a question from former MLA Trevor Lunn who said smuggling could involve retail goods and the "old favourite" - cattle and pigs.
The officer said 43% of organised crime by gangs in Northern Ireland "has a cross-border dimension. Some of that is drugs-based, and some is commodity-based or based on human trafficking".
"There already is a well-trodden path between the two jurisdictions on criminality, so any separation on immigration or tariffs will certainly create an opportunity and, in the mindset of our crime gangs, an intent to perhaps exploit those tax or immigration differences," he said.
"As well as the other criminality they are involved in, there will just be another commodity tacked on to their existing activity," Mr Hume added.
"It is something we have identified and recognised, and we are engaging with our partners to understand the threat around it.
"As you say, already, through the cross-border task force, a lot of work goes on in that activity as we speak."