I don’t know what causes this problem but recently I discovered that the “Default web browser” setting in the General preferences tab was blank. Clicking on the drop-down showed no browser names so I could not change the use of Safari as the default browser.
The fix was relatively simple. I opened Chrome and via settings within Chrome I set it to be the default web browser. After completing this action I then had the names of the installed browsers in the “Default web browser” drop-down.
This fix may work using any browser that allows you to set it as the default from within the browser settings itself.