Still suspicious, I followed his instructions and clicked on computer management and saw warnings where he said I would and accepted that this was a genuine call. He told me to highlight certain items in the list and delete them. I tried but wasn't able to delete them and he told me to open Internet Explorer so that he could help me directly. Fortunately for me, broadband in rural areas is poor and using my landline disrupts the internet connection. I couldn't get online. I asked the advisor to call me on my mobile but he said he wasn't allowed to do that but gave me a number to call him back on. Again, fortunately for me, the reception was poor and I said I would get help from someone else and rang off.
This is what I discovered when I rang PC World's TechGuys:
Microsoft do not have your personal details
Microsoft never call you
If I had managed to get online the bogus caller would have either gained access to my passwords etc or got me to download a virus