All your answers were helpful. I thought a report would be useful to others with the same question.
PHV - CASE appears to exist to provide multiple 'exits' depending various values of <substring>. As I was only after a YES or NO result I decided not to use this. But prompted by your suggestion I have read up on CASE and better understand it, and no doubt will use it in the future, so thank you for the suggestion.
aau - My problem matches your VARIABLE=abcdef, SUBSTRING=def example. Apologies for not making this clearer. I was successfully able to write my statement along the lines of your example. Thank you for the suggestion.
SamBones - I can confirm that the @(Pattern) construct worked successfully. You confused me a little by calling a hash (#) 'a pound sign' rather than a (£). I presume you must be writing from somewhere abroad of the British Isles?
I ended adopting the following simple syntax that I discovered worked -
If [[ $<VARIABLE> != *<substring> ]]
Where the asterisk (*) represents all characters at the beginning of the string being tested, and <substring> represents the characters at the end.
...unless I have misunderstood of course?