Thank you, both Tim and Bob, for your replies.
Mostly I work in RGB because the vast bulk of stuff I produce is printed on an inkjet printer and there is nothing to be gained by working in CMYK for an inkjet — indeed, because the monitor is always in RGB, colours are only an approximation so there is some loss. The only time I use CMYK is if I am producing something to go to a commercial (usually web offset) printer.
The use of the Direct Selection Tool (whose name I can never remember so I call it simply “the white arrow”) is the hint I needed. It works a treat with greyscale images and also, of course, with b&w bitmaps. What a pity it doesn’t work with Illustrator files. I use these fairly frequently and, if ever I need to convert one that is in black and white to colour, I still need to go back to the original .ai file and change the stroke and fill colour of every single item in the image. Is there a quicker way to do that? Is there some way to do it in InDesign?
I have been using InDesign since version 2.0 and I am still learning!