Sometimes it's just a case of persuading iTunes to actually Stop rather than Pause
When you first launch iTunes it is Stopped - the top menu doesn't contain any current song info. If at that point you hit Play, it will actually start from just the first song in the list & continue on down the page [assuming you don't have shuffle enabled, of course].
If you double-click any track instead, then it will do the same, from that track - which is what you want...so...
To make it actually Stop, whilst it's playing, hold Alt ⌥ & click the Pause button II
You might also notice the rewind button changes to a kind of 'orbiting' icon - that's to start Genius based on the current track - but not relevant to this issue.
Once stopped, it ought to return to 'normal' behaviour.
If it doesn't, an alternative is to enable, then disable shuffle. That should also revert to linear play mode.