Media playback is unsupported on your device Media caption Why the fuss about the European Court of Justice?

Theresa May has insisted the jurisdiction of the European Court of Justice in the UK will come to an end with Brexit.

As the government published new details of its position, the PM said the UK would "take back control of our laws".

But critics say it will be impossible to avoid European judges having a role in enforcing new agreements drawn up with the EU.

Ministers say the two sides will keep "half an eye" on each other's rulings.

The ECJ is in charge of ensuring member states abide by EU law.

Its rulings are binding on all member states, and it also settles disputes between countries and EU institutions.

In its new policy paper, the government:

Does not rule out ECJ keeping its jurisdiction during the Brexit transition period that is planned after March 2019

Promises to work with the EU on the "arrangements for judicial supervision" during this period

Makes clear that the rights of EU citizens living in the UK after Brexit will only be subject to British law - a sticking point in the negotiations with the EU

Says giving the ECJ authority over UK-EU disputes would be unprecedented and not "fair and neutral"

The promise to end "direct jurisdiction" in recent policy papers - a phrase not used by Mrs May - has raised questions about what "indirect" jurisdiction the EU court could be left with.

In the latest publication, about how to enforce disputes after Brexit, the government has outlined several models used by other countries that it says show there is no need for the ECJ to be the final arbiter.

But some of these involve the ECJ having an influence on the outcome of disputes, for example by interpreting EU law in a way that binds a disputes panel, or for its past rulings to be taken into account.

Analysis

By BBC Legal Correspondent Clive Coleman

Today's paper does not pin the government's colours to any particular mast.

It throws out a number of possible models for how a trade agreement with the EU would work in terms of resolving disputes.

All of the models make it clear that the ECJ will no longer have sole jurisdiction over disputes.

The key question is how much influence the ECJ would retain under a bilateral agreement with the UK.

The EU will not sign up to an agreement which allows to UK to depart from EU law to the UK's advantage and the EU's disadvantage on things like state aid to companies, or emissions standards.

It will want a level playing field in trade and that will mean a lot of EU law as part of the agreement.

The reality is that the more closely the Brexit trade agreement replicates EU law, the greater the influence of the ECJ will be.

Labour leader Jeremy Corbyn said the government was "clearly backtracking on its earlier red lines and saying there has to be some form of dispute resolution through some form of judicial process".

He added: "We have said that all along."

Asked if Labour would vote against the government's key piece of Brexit legislation, the repeal bill, when MPs returned from their summer break, Mr Corbyn said: "We will make that decision just before the vote."

The pro-EU Open Britain campaign group said the government's policy paper was a "climbdown camouflaged in jingoistic rhetoric".

The group called it "frustratingly vague", adding that in almost every example it provides, the ECJ would have "substantial direct or indirect power over the proposed new relationship between Britain and the EU".

The government said it was not committing to following any of the arrangements set out, ruling out an "off the shelf" model.

And sources played down the significance of the word "direct", saying it meant ECJ rulings would no longer automatically apply to the UK and that the court would no longer be able to strike down domestic UK laws.

Media playback is unsupported on your device Media caption John Redwood and Chuka Umunna clash over ECJ

Asked about her government's position, Mrs May said: "What we will be able to do is to make our own laws - Parliament will make our laws - it is British judges that will interpret those laws, and it will be the British Supreme Court that will be the ultimate arbiter of those laws."

Earlier Justice Minister Dominic Raab said there would be "divergence" between UK and EU case law after Brexit, adding: "It is precisely because there will be that divergence as we take back control that it makes sense for the UK to keep half an eye on the case law of the EU, and for the EU to keep half an eye on the case law of the UK."

In response, Guy Verhofstadt, the European Parliament's lead negotiator, tweeted that the ECJ had to "keep both eyes open" to protect citizens' rights.

The ECJ's remit extends into many of the areas where the UK is hoping to draw up new arrangements with the EU, including trade and citizens' rights.

Mr Raab said "some form of arbitration" would be needed, but that this would not be akin to a European court.

Arbitration is where disputes are settled by a neutral third party. The UK and the EU could each appoint arbitrators and agree on a third, Mr Raab suggested.

Image copyright AFP

European Court of Justice

Decides whether the institutions of the EU are acting legally, and settles disputes between them

Ensures that the member states of the EU are complying with their legal obligations as set out in the EU treaties; and allows member states to challenge EU legislation

Interprets EU law at the request of national courts

The SNP said the government had accepted the UK must continue to take account of judgements from the ECJ so it now needed to "ditch their previous so-called red lines to ensure a deal can be found".

SNP External Affairs Secretary Fiona Hyslop said the best option for Scotland and the rest of the UK was to stay in the EU single market.

Liberal Democrat leader Vince Cable said Mrs May's "red lines are becoming more blurred by the day", saying the ECJ had "served Britain's interests well" and should not be "trashed".

The European Commission, which is leading the negotiations for the EU, did not comment in response to the government's publication.