After some tinkering, I have found that that was the problem.
I had the setting for the side switch to lock the rotation rather than mute.
This worked fine for locking and unlocking screen rotation but had a strange effect on mute.
Whether it was on or off, system sounds were muted.
Therefore, I changed the setting to Mute instead of Rotation Lock. This got me back the sounds.
Once I knew system sounds worked, I then switched Rotation Lock back on and, hey presto, everything OK.
Never even noticed the Mute icon to the left of playback controls (double home and swipe right). Perhaps that would also fix it.
Thanks for your pointer JimHdk - you were a great help.