Theresa May, the home secretary, said this week Britain should leave the European Convention on Human Rights, a 1953 treaty that has generated decades of headlines but is separate from the EU.

Many Eurosceptics are much more exercised about an agreement that is part of the bloc and which has real and growing power over British laws.

The Charter of Fundamental Rights lays out the basic rights of EU citizens. These are enforced by the European Court of Justice, the EU’s highest court, which, in recent years, has become more activist.

As the June 23 in-out referendum approaches, both the charter and the court are at the heart of the argument that Britain needs to leave the bloc to end a state of affairs in which EU law trumps its own legislation.

The charter had no legal status until it was incorporated in the EU treaties in 2009. But last year it was invoked in at least 56 UK cases, ranging from the confidentiality of Prince Charles’s letters to government ministers to official plans for plain packaging for cigarettes.

British lawyers are increasingly citing EU law, which has primacy over UK law, to win their cases. The number of references to the charter in leading EU court rulings has also risen sharply, from 43 in 2011 to 210 in 2014.

While supporters say the charter and court do no more than set out and enforce European law, the Brexit camp says both have hugely increased the scope of that law, shackling the autonomy of British institutions.

Dominic Raab, a justice minister, said the decisions of the ECJ “affect everything from the price of beer to the cost of home insulation” and “undermine the basic principle of our democracy — that the British people can hold to account those who write the laws of our land”.

The charter has spawned a host of new rights with profound consequences for British courts, critics say, just as the ECJ’s role has grown beyond policing the EU’s single markets to take in human rights and asylum cases.

In the common market days it was just enforcing the consensus, now it is enforcing policies with which we don’t agree

Dominic Grieve, a former attorney-general, the British government’s chief legal adviser, accuses the ECJ of expanding its area of competence for ideological reasons. “It sees itself as bringing about ever-closer union,” he said. But he suggests the court may now be more respectful of British law because of a pre-referendum deal to exempt the UK from that longstanding EU goal.

Others express no such hope. David Davis, a senior Conservative MP who wants to leave the EU, called the ECJ an intrusive but “inevitable part of being in the EU”.

“In the common market days it was just enforcing the consensus, now it is enforcing policies with which we don’t agree,” Mr Davis said.

While European law has had primacy over British legislation since the day Britain joined the European Economic Community in 1973, senior British judges have also been outspoken on the ECJ’s growing role. “We should be under no illusions: the jurisdiction of the Luxembourg court covers far more than economic matters,” said Lord Dyson, one of the most senior judges in England and Wales, in a 2014 speech. “It affects many parts of our national life.”

Supporters maintain that European judicial activism has been exaggerated and the charter is only intended to enshrine existing rights and to curb the power of European institutions.

Far from being expansionary, they say, the ECJ has stepped back from ruling on certain issues — including the legality of public spending cuts in EU countries such as Portugal and Ireland.

“Some of what has been said about the influence of the EU charter is overblown and inaccurate,” said Damian Chalmers, professor of EU law at the London School of Economics.

Lord Goldsmith, who as attorney-general negotiated a supposed “opt-out” of the charter on behalf of Tony Blair’s Labour government, said “the EU charter only reflects existing law in any event; it doesn’t grant new rights”.

But in a 2015 case involving workers at two embassies in London, the UK Court of Appeal acknowledged that the charter invests pre-existing rights with greater powers because of the primacy of EU law.

In allowing Fatima Benkharbouche and Minah Janah to pursue claims of illegal hours and inadequate pay, three appeal judges in effect overturned Britain’s law on diplomatic immunity in favour of a charter principle, in this instance the right to a free trial.

The charter’s provisions on the right to a free trial are based on an article of the ECHR. But, looking to the ECJ for guidance, the Court of Appeal found that the mere fact that those provisions now appear in the EU lawbook allows them to overturn British law.

We should be under no illusions: the jurisdiction of the Luxembourg court covers far more than economic matters

Similarly, long established principles of British law — such as the right to strike — may take on added force because of their inclusion in the charter. Paul Craig, professor of English law at Oxford, told MPs in 2014 that the charter gave such pre-existing rights “a degree of peremptory force that they would not otherwise have had”.

Supporters say that giving privileged status to human rights should not be cause for criticism — and that, as in the instance of embassies employing the two North African women, it ensures that nobody is above the law.

Opponents argue that the true power of both the charter and the ECJ has been consistently underestimated and that there is only one option to break free of their burgeoning influence — to leave the EU.

The EU’s Charter of Fundamental Rights is a product of the first decade of the 21st century, when efforts at European integration reached a peak.

Drawn up by a special EU convention in 2000 to set out a range of existing rights in a single text, the document was incorporated into the bloc’s plans for a draft constitution.

Although the constitution was rejected by French and Dutch referendums in 2005, the charter finally became legally binding in 2009 as part of the EU’s Lisbon Treaty.

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Many of the charter’s 54 articles come from the ECHR, including provisions on respect for private life, the right to a fair trial and freedom of religion.

But some lawyers say the charter’s provisions are broader — for instance, it sets out the right to marry without reference to men and women, potentially covering same-sex marriage.

The ECJ’s rulings on the charter are binding on all EU members.

Some of what has been said about the influence of the EU charter is overblown and inaccurate

By contrast, the Strasbourg-based European Court of Human Rights, which rules on the ECHR, can be brushed aside by parliament and need only be “taken into account” by judges.

The settled case law of the ECJ holds that the fundamental rights set out by the charter apply “in all situations governed by EU law, but not outside such situations”.

Nevertheless, the ECJ ruled in 2013 that it did apply to the case of a Swedish fisherman prosecuted in his own country for incorrectly reporting income, because the case was “in part” connected to value added tax, which helps finance the EU budget. That ruling led Lord Mance, a senior British judge, to remark: “There are therefore few limits to the dominance of EU law.”

Some experts note that the charter and EU law naturally applies to cross-border cases involving citizens of other EU states, but have no bearing, for example, on deportation orders for citizens of third countries outside the bloc.

One sensitive area covered by the charter and EU law is data protection.

Mr Davis has challenged new UK legislation on the police and intelligence agencies’ access to internet and phone data.

The UK High Court found the measure was “inconsistent with European law”; the Court of Appeal referred the case to the ECJ and the Luxembourg tribunal’s decision will be final.