The phone booth trick was to hold a recorder to the earpiece when you put in your money. back in the days of pulse-tone technology, the earpiece would play a small "blip" noise,
I worked for BT at the time that was happening. The trick was to get voicemail, which meant you were given a free digital tonepad to pick your messages up from a non-digital phone (which nearly all phones were in those days. The tonepads were also on sale in some electronics stores.
If you used the tonepad in an old telephone box, you didn't have to put money in, and could make international calls. The worst offenders were students from overseas, and paradoxically BT staff, who all knew about it and all had a tonepad.
You're right that it hasn't worked since about 1993 - when I left in 92, they were rushing to fix the situation.
There was also a huge amount of cellphone cloning in pre-SIM card days - that could be done using a paperclip and a bit of tinfoil, by anyone who knew the serial number and mobile number of a phone. Pre-1985, the old 'system 4' carphones relied on honesty for the billing (when you picked them up, the connection went straight to an operator who asked for the number and timed the call), and since they were mostly used by businessmen, honesty was by no means universal.