The UK government's "future partnership" paper made a strong case for "a bespoke relationship with Europol" after the UK leaves the European Union.
It looked at the scenarios of:
- no agreement being reached on future cooperation with Europol
- current cooperation being wound down before a new arrangement was put in place
It said: "Consideration would need to be given to ensuring that any ongoing investigations would not be affected in such a way that criminals might escape prosecution or vulnerable individuals might be rendered less safe."
And it would be difficult to find anyone in the EU who would disagree with the importance of fighting cross-border crime.
Europol, the European Union's law enforcement organisation, was founded in 1999 and employs more than 1,000 people at a cost of about £100m a year.
It is an EU-funded agency, and when the UK completes the Brexit process and no longer pays into the EU budget, it will cease to be a member.
The EU's chief negotiator, Michel Barnier, used an article in the French newspaper Le Monde to make it clear the UK could not continue to be a member.
He said: "The British defence minister will no longer be able to sit at the council of defence ministers, London will leave the European Defence Agency and Europol."
Prime Minister Theresa May has previously said she wants the UK to retain its security co-operation with Europol post-Brexit.
And a number of countries that are not part of the EU, such as Norway, Switzerland and the US, have operational agreements with Europol that allow access to intelligence.
But Europol itself say this does not equate to formal membership, which means these countries do not have a say over operations and decisions.
Europol also points out that such agreements take a number of years to negotiate.
One precedent that might act as a future model is Denmark, an EU member but no longer in Europol.
In December 2015, Denmark voted in a referendum against more integration of security operations.
In May this year it formally left Europol, but an agreement was reached that allowed the Danish police and Europol to continue to share information and analysis.
Denmark is able to participate in Europol board meetings, but it has only "observer status" and no decision-making rights.
Could a similar agreement be made with the UK?
Europol seems to think not. In a statement, it said: "The agreement between both Denmark and Europol is based on the fact that Denmark is a full member of Schengen [group of countries that allow passport-free travel] and has implemented all EU data protection standards.
"It therefore allows for a sufficient level of co-operation, including the exchange of operational data and the deployment of liaison officers."
Prof Alan Woodward, a British cyber-crime expert and adviser to Europol, said the issue of the UK's future relationship with Europol needed to be resolved sooner rather than later.
"I very much hope that a solution is found to allow the UK to remain active participant with Europol - simply because it is in everybody's interest," he said.
"Europol is the best organisation to tackle cross-border law enforcement issues, especially in cyber-crime."