The Government has said it is in everybody’s interest for co-operation with Europe on security matters to continue after Brexit.
The European Arrest Warrant has helped apprehend thousands and has been an important tool for police on both sides of the Irish border pursuing fugitives.
Under-secretary of state in the Brexit Department Robin Walker said he would have preferred negotiations to have made greater progress on security matters.
He added: “We are pushing ahead with a very ambitious approach to the future security partnership.
“All the evidence is that there is very strong interest in continuing co-operation in this area.”
He gave evidence to the House of Lords EU Select Committee in Westminster.
“We do think that when people take a long, hard look at this they will recognise it is in the EU and in the UK’s interests for these mechanisms to continue.”
The Irish border is one of the most vexed issues still facing negotiators in Brussels.
The Police Service of Northern Ireland (PSNI) enjoy a close working relationship with their Garda colleagues on the frontier.
PSNI chief constable George Hamilton has said he is drawing up a business case for extra resources which may be needed to police the more than 300 miles of border and hundreds of crossing points.