Human rights groups have long been trying to challenge the mass surveillance activities of the British intelligence services. Now, having failed to get meaningful reform from courts in the U.K., they have asked the European Court of Human Rights (ECHR) to put its foot down.

Ten groups, including Amnesty International and Privacy International, on Thursday filed a case with the ECHR over the U.K.’s own mass surveillance activities, and over its access to U.S. mass surveillance programs.

They said the reaction to Edward Snowden’s revelations had not gone far enough, and decried the U.K.’s activities—particularly the way it intercepts huge amounts of data traveling over the Internet cables that cross its territory.

“For years, the U.K. government has been secretly intercepting enormous volumes of internet traffic flowing across its borders. At the same time, it had and still has access to similarly vast troves of information intercepted by the U.S. government,” said Privacy International general counsel Caroline Wilson Palow, who noted that U.K. courts have allowed this to continue.

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“We call on the European Court of Human Rights to reject this disturbing trend by finding that bulk surveillance is incompatible with the rights to privacy and freedom of expression enshrined in the European Convention on Human Rights.”

The American Civil Liberties Union (ACLU) is also involved in the case. ACLU staff attorney Ashley Gorski said that bulk surveillance was not only unlawful, but that it also “has a deeply chilling and corrosive effect on political discourse and our personal communications.”

European privacy law is supposed to forbid surveillance that is not targeted to specific people, and that is disproportionate.

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The European Court of Human Rights’ rulings are legally binding, although the U.K.’s Human Rights Act states that British courts need only take those rulings into account—they don’t technically need to comply with them, although the British Parliament does have to comply with them. (Yes, it’s complicated.)

Whether or not the U.K. pays attention to the European court’s ruling, the human rights groups noted that the ruling would also provide “guidance” for the 47 Council of Europe states that fall under its jurisdiction—that means not only the EU but also countries like Russia and Turkey.

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The groups that lodged the case include: Privacy International, the American Civil Liberties Union, Amnesty International, Bytes for All, the Canadian Civil Liberties Association, the Egyptian Initiative for Personal Rights, the Hungarian Civil Liberties Union, the Irish Council for Civil Liberties, the South African Legal Resources Centre, and Liberty.

In the wake of Snowden, Privacy International took its case to the U.K.’s Investigatory Powers Tribunal, which is supposed to provide oversight for the intelligence services.

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The tribunal ended up ruling that the U.K. government’s access to U.S. mass surveillance data had been illegal before Privacy International’s case, but was legal after it because the arrangement was no longer secret.

It also found that the U.K. government had unlawfully spied on Amnesty International and the Legal Resources Centre. However, it said mass interception was lawful in principle.