How can one listen to radio versions of the Top 40 from the 1980's?

You can listen to 1980 Top 40 radio versions from many different websites; musical and radio archives are a good place to start. If, however, those services cannot be accessed by yourself, you can listen to modern radios such as Radio 2 which goes back and repeats the Top 40 songs from different eras (for example, the 1980's).