Britain’s most senior EU official has warned that a post-Brexit Britain would have to recognise the rulings of the European court of justice if it wished to maintain the current level of cooperation in countering terrorism and organised crime.

Sir Julian King, the European commissioner responsible for security, said the UK’s security services had become increasingly reliant on shared crime-fighting tools to carry out their work.

In an interview with the Guardian, King suggested that there would be difficult discussions to be had in order to maintain something near the status quo on security cooperation, which will form part of negotiations with the remaining 27 members of the EU.

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The bloc unanimously agreed this weekend a tough set of negotiating guidelines, including the declaration that the EU would not discuss trade matters or security cooperation until the issues of Britain’s divorce bill, citizens’ rights and the border on the island of Ireland were settled.

At the Brussels summit on Saturday, both the president of the European commission, Jean-Claude Juncker, and the German chancellor, Angela Merkel, indicated some concern that this message had yet to be understood in London.

Over dinner, Juncker is said to have pulled out a copy of the EU-Canada trade deal, a document of 2,000 pages that took nearly a decade to negotiate, and suggested Theresa May study its complexity.

It has been claimed that at a meeting between Juncker and the prime minister on Wednesday in Downing Street, May asked for a full outline of a future trade deal before agreement on an estimated €60bn withdrawal bill was arrived at. One EU diplomat was quoted by the Sunday Times as claiming: “This was a rather incredible demand. It seemed as if it came from a parallel reality.”

On Sunday, May was tackled about reported comments from Juncker that she was living in another galaxy when it came to her demands for trade talks before the exit bill was settled.

The prime minister denied this was the case. “I’m not in a different galaxy but what this shows is that there are going to be times when these negotiations are going to be tough; we need strong and stable leadership.”

She insisted she was still confident the UK could get a trade deal, saying: “I want to ensure that we agree on a trade deal and our withdrawal arrangements so we know what both of those are.”

King told the Guardian that in order for security cooperation to be maintained, the EU institutions would need to break new ground and there may be tough political compromises to make on either side, including over the role of the ECJ.

In the latest example of the work of Europol, the UK joined 16 other member states earlier this year in uncovering the identity of child victims of sexual abuse posted on the internet.

“The UK has exported 8,000 people under the European arrest warrant and imported a thousand, it is an active user, but there you are talking about an element of the acquis [EU law] and legal and criminal proceedings, so you have to have some level of arbitration,” King said. “The existing level of arbitration is the European court of justice, so that is an issue that will have to be worked through in the negotiations.”

He added that it may be possible for a new independent arbitration body to be established to avoid the ECJ being directly involved, but that it would be rulings made by the court in Luxembourg that would be at issue when the new body came to adjudicate. “By definition the jurisprudence relating to the European arrest warrant is ECJ jurisprudence,” he said.

Along with leaving the single market and ending the free movement of people, Theresa May has set taking back control of British law and ending the jurisdiction of the ECJ as a test of whether the UK has left the bloc.

A softening of Downing Street’s position on the ECJ would be likely to be fiercely resisted by some senior Tory MPs, who accuse the the court in Luxembourg of eroding British sovereignty.

Asked whether he agreed with the prime minister that no deal with the EU would be better than a bad deal, King said: “You are not going to get me to comment on aspects of the UK government’s position. From the commission’s point of view on terrorism, cyber and serious organised crime, we have a shared assessment of the threat and we are stronger countering them if we are working together.”

King, a former ambassador to France who was nominated last year by David Cameron for his post in Brussels following the referendum, said the European commission believed continued cooperation on security was in everyone’s interests, and the European council’s negotiating guidelines outlining the EU’s negotiating position indicated a willingness to come to a deal.

He added that the UK’s decision last year to opt back in to Europol, which from Monday is more firmly under the control of the commission and has greater flexibility in sharing criminals’ data, suggested the UK felt the same.

Up to 40% of traffic through Europol comes from the UK or concerns issues involving the UK. Between 2015 and 2016 the number of enquiries the UK made of the Schengen information system, which holds an 8,000-name watchlist of suspected terror suspects and is used to monitor those coming in and out of the EU, increased by 100%.

But King said: “At the moment there are no precedents for non-EU member states having a link to the Schengen information system. So if the UK wanted that, it would have to be something to be discussed, it would have to be a particular bespoke arrangement.

“There is no precedent for such a thing. You get into the wider issue of data protection rules and data adequacy. An overall arrangement on data adequacy, ie the EU recognising that it accepted the level of data protection in the UK.”

King, who will be the last commissioner from Britain in Brussels, added of membership of Europol: “Just because you want something doesn’t mean it is easy.

“Full membership as such, at the moment, is available to EU member states. So it would have to be, if the UK wanted it, subject to discussion and agreement with the member states, something new and different, the terms of which and how that operates would have to be agreed.

“The issue that at some point will need to be confronted is two years down the track, if you don’t have something sorted out for the day that there is a change, then you have a problem and a potential gap.”

Denmark opted not to be a member of Europol, and has come to an arrangement under which it is able to ask for data, rather than have direct access. “They have to present effectively a request to Europol to say: ‘We would like to be working with you on this, that or the other,’” King said. “It is obviously short of the situation that member states are in and the UK is in, having opted in to the new regulation.” The Danish position was “workable”, he added, but it “does make it a bit more cumbersome to organise your security”.