I got hold of a small transistor radio and noted that the FM tuning capacitor had a couple of fixed capacitors connected in parallel. I gently unsoldered these and Bingo! the radio was tuned to the aircraft band.
Would this be possible on any radio? Eg. an old Sony cassette FM/MW radio?
Highly unlikely. The aviation band, although close to the commercial FM band is AM not FM so I doubt this would have really worked. Even the cheap airband receivers are rubbish. Personally I'd save your money as listening in to other transmissions is either one sided (you won't hear the ground station unless you are fairly close to it) and also full of inappropriate RT chatter for a new PPL. Most of the time you'll hear heading/height acknowledgements on the airways where you really want to be learning joining instructions & MATZ penetrations etc.
Spending an hour in your local tower will be much more worthwhile.