The disclosure comes less than a fortnight after the European Court of Human Rights ruled that the methods used by GCHQ to collect information through bulk interception of online communications violated privacy and did not provide enough safeguards.
A statement from Privacy International said the agencies had denied on more than one occasion that their programs were the equivalent of mass surveillance of people who were innocent of any crime.
The mea culpa from the British agencies occurred during the course of a challenge by Privacy International to the powers for the BPD and BCD programs before the Investigatory Powers Tribunal, a court that hears claims against British intelligence services.
Privacy International's general counsel Caroline Wilson Palow said: "Today's revelations are troubling for a whole host of reasons. The UK intelligence agencies' bulk collection of communications data and personal data has been shown to be as vast we have always imagined – it sweeps in almost everyone, including human rights organisations like Privacy International.
“Not only was Privacy International caught up in the surveillance dragnet, its data was actually examined by agents from the UK's domestic-facing intelligence agency – MI5. We do not know why MI5 reviewed Privacy International's data, but the fact that it happened at all should raise serious questions for all of us.
"Should a domestic intelligence agency charged with protecting national security be spying on a human rights organisation based in London? Shouldn't such spying, if permitted at all, be subject to the strictest of safeguards? In an era when human rights and democracy are under threat all over the world, the UK should demonstrate leadership by protecting human rights defenders.
“Privacy International therefore urges the UK Government to critically examine its mass surveillance powers, as enshrined in the Investigatory Powers Act 2016. They have now been called into question twice in two weeks - by today's revelations and by last week's judgment from the European Court of Human Rights.
"The UK should be a beacon of light in a world where democracy is under threat. Its refusal to curtail the mass surveillance powers of its intelligence agencies casts a shadow over all of us."