Searched high and low only to find you cannot see a list of recently played songs via the app.
As many of you have probably experienced I heard a song on Release Radar and forgot to save it and couldn't remember the name!
I have found what may be useful for people in the same position.
Go to any playlist on your app and you will see a button labelled "Add Songs" just below the playlist album cover. Once you click on this it provides you with various songs to add but if you scroll right to the third list along it will show you dozens of your recent played songs and hopefully allow you to find that one song as I now have!
Hope this may help as I know not everyone uses the desktop app but would be great if it could be officially implemented by Spotify at some point.