I uninstalled everything 'Adobe' from 'Programs' on my hard drive.
This resulted in no crashes - but no facility to read PDFs.
I reinstalled Adobe Reader (and was prompted to download and install Adobe Download Manager (seemed to be associated with the browser) and the 'crashing' of the browser returned when I tried to download a PDF. It seems to be when the PDF is attempted to be 'read' by the browser (which seems to happen automatically rather than requiring Adobe Reader after 'saving').
I'm currently using the 'safe' laptop but I intend returning to the 'dodgy' one and altering the DEP settings.
Thanks for the advice, folks.