Ms Dick said she hopes police will have “as much as possible of the instruments” they currently have after Brexit. Britain’s most senior police officer added there would be cost and public safety consequences of having to replace the systems.
Asked about a no-deal Brexit, Ms Dick said the UK works closely with the EU at the moment.
She told BBC Radio 4’s Today programme: “If we come out without immediately obvious replacements for those instruments, that will undoubtedly mean we will have to work incredibly hard on a bilateral basis with countries to try to get in place some kind of way of working together.”
Ms Dick said that talks are ongoing, adding: “We’ve set up an EU co-ordination unit, absolutely.
“That is to help local forces to understand to how to work most effectively across Europe after we exit the EU, under whatever circumstances.
“Of course, we would hope we will have as much as possible of the instruments we currently have or something very similar as quickly as possible in order to be able to keep our public safe and at the same sort of cost.”
Told she was suggesting the consequences of not having such a situation would mean the UK is less safe, Ms Dick replied: “The consequences are that we will have to replace – and of course if there was a no-deal scenario that would be very difficult to do in short-term – some of the things we currently use in terms of access to databases, the way in which we can quickly arrest and extradite people, these kind of things, we will have to replace as effectively as we can.
“That will be more costly undoubtedly, slower undoubtedly, and potentially yes put the public at risk – no doubt about that.
“But I understand that this is just one of many things that the politicians who are deciding what to do next have to think about.”
The warning comes weeks before MPs are set to vote on Theresa May’s Brexit agreement, after the first vote which was due to take place in December was cancelled over fears ministers would reject it.
Britain is due to leave the EU on March 29, two years after the Government triggered Article 50.