It does not seem that McAfee is actually running any scans! 'History' shows a series of successful updates, but no mention of any scans, although I have Scheduled Scan set to 'daily'. Clicking 'start' on the Full Scan tab brings me 'initialising Scan' but nothing further. The Custom Scan tab shows only an option for a full scan - I thought I was able to select other options. Clicking 'start' gives the same result as the Full Scan tab.
Solved! I got in touch with BT Customer Care, who advised deleting and re-installing. Which did the trick! Except - along the way I was invited to install McAfee/BT Virus Protect on my iPhone and iPad. I tried, was sent install links which were for Android, rather than IoS. Back to BT, more time spent on online chats/phone calls, until I was eventually told that 'due to circumstances beyond our control, BT Virus Protect is not avaiable for the IoS platform'. It would have been nice if that was made clear on the website. BT really is not Mac-friendly, is it?