Thank you for your reply.
I'm disappointed but --- "No big deal". I have had a work-around right since Day One --- one of my top level tiles in Speed Dial is reserved for search engines (Start Page, Duck Duck go, scientific databases, etc.). So anonymous searching is available via two mouse clicks instead of one, as would have been the case had it been possible to customise the Search Box.
Now that I am retired (I'm 83) I spend a lot of time on-line researching scientific topics so I like my browser to be customised to my personal idea of how the interface should look --- which is why I have stuck with Firefox for so long. With that said, Opera is very nice and I have presently got it set as default but Firefox is still available via a launcher on my Desktop. One of the things I admire about Opera is the way it imported my bookmarks from Firefox. I have well over a thousand of these, all in folders, several layers deep and Opera has preserved the organisational structure. This is a huge bonus point, so far as I am concerned.
Thank you once again --- Best regards from the UK