http://www.dself.dsl.pipex.com/museum/COMMS/ear/ear.htm

As you can see, by the time they were becoming obsolete in the 1930s, they were looking like they were designed by H.R.Giger. However my previous comment was wrong in one respect: in WW2, they did continue to be used for a short time for one specific role: aiming searchlights (for this, it obviously doesn’t matter that the detection range is not very far.) However by not too far into the war radar sets were being made cheap enough and small enough to mount on searchlights.

By the mid-1920s, aircraft were getting so fast and high-flying that to get adequate detection range, the British had started to experiment with the gigantic concrete versions whose remains are still found along the Channel coast. Those huge acoustic lenses fed into electronic amplifiers and electronic engine-frequency detectors. But by the 1930s — before the system was actually deployed — they were already obsolete as the best acoustic detection technology was inadequate for the latest planes. A lot of effort went into exploring alternatives (including infra-red thermal detection, which couldn’t be made to work properly at the time but was in service by then end of WW2) and radar was invented.

There was no reason for the British to pretend that their detection system wasn’t radio based. The Germans also had radar, and knew perfectly well that the British had it too. However the British did manage to continuously fool the Germans about their exact radar capabilities, which for most of the war stayed a couple of years ahead of the Germans in most respects. (And, indeed, a decade ahead of the rest of the world until the Churchill sent Sir Henry Tizard to share advanced British technology with America.) The deception games they played are fascinating, but a lot more complicated than just pretending they didn’t have radar. If interested, you can read about it in “Most Secret War”, the memoirs of Dr. R. V. Jones, one of the scientists involved.