A "gargantuan" effort would be required to remove key EU-wide bodies from the jurisdiction of the bloc's highest court, according to an expert.
Cambridge University professor of EU law Catherine Barnard said it is clear the treaty behind the European civil nuclear regulator, known as Euratom, gives the European Court of Justice (ECJ) the official power to make legal decisions and judgements.
She added the ECJ also has jurisdiction over matters involving EU agencies, such as when challenges are made against decisions by the 40 or so bodies - which include the London-based European Medicines Agency.
But Prof Barnard said there is a lengthy amendment procedure in place, including referendums being held in several countries, should attempts be made to amend the EU's fundamental treaties to remove references to the ECJ.
Her final remark came after she was asked what would happen if the UK asked to retain access to certain EU-wide bodies but without ECJ involvement.
Prime Minister Theresa May has made leaving the remit of ECJ a "red line" for Brexit negotiations.
Her decision to pull out of Euratom, which is not formally part of the EU despite being under the jurisdiction of the ECJ, has prompted Tory unease and fears among MPs about risks to high-skilled jobs, cancer treatment and the nuclear fusion supply chain.
Speaking at an Institute for Government (ISG) event focused on Brexit, dispute resolution and the ECJ, Prof Barnard said: "These agencies... are firmly bedded in the institutional structure and dynamics of the European Union, and of course why wouldn't they be - they are institutions, agencies of the European Union and they were set up with the EU system in mind."
Former senior civil servant Jill Rutter, the ISG's programme director who chaired the event, asked: "If we wanted to have a slightly pick n mix variation and take some of these things but without ECJ, you're basically saying 'Hello EU, you need to amend the fundamental treaties of the European Union to take out references to the ECJ or to amend them'?"
Prof Barnard replied: "Absolutely, which would be under the lengthy amendment procedure which would require referenda in a number of countries - I mean this is a gargantuan exercise."
The professor also said attempts to take back control by the UK will be "partial" as a "deep and special" trading relationship will need someone to "set the rules of the game and to ensure the rules of the game are arbitrated upon".
She said: "So there'll need to be some supranational body and thus taking back control, by definition, will be partial.
"Now we already concede that through the WTO panels system, there are all sorts of other supranational bodies that we give deference to.
"But the fact is, if we're going for a deep partnership there will need to be somebody who acts as referee in some form."
Michael-James Clifton, chief of staff to the president of the Court of Justice of the European Free Trade Association (Efta), told the same event: "The experience of the Efta states is that's been a great advantage to have an own court.
"A court provides a gateway to justice for companies and individuals that state-to-state arbitration cannot.
"Whether the UK proposes to create a new tribunal is a matter for the Government.
"But I think, from my personal perspective, it'd be well advised to seriously consider docking to the Efta court for both the transitional agreement - potentially through the European Economic Agreement - and the sought deep and special partnership."