Whilst waiting for your response Gary, I decided to re-install my old 7290 and see if the same problem exists when using that device.
Nope, everything worked perfectly well on the 7290 - received all emails from all accounts as expected.
So, looks like the problem is definitely with my 8310 handset (just why it is not receiving one particular email acount is anyone's guess
) and the firmware upgrade is my only chance of resolving the problem.
Look forward to receiving your instructions, links and tips, Gary.