That notice shows that some of the page is from secured connections while part of it is not.

What do I have to do to stop this coming up with all kinds of web sites? You help pages talk about deleting cookies, but I've no idea what ones. I am fed up with this happening and am thinking of changing to Google chrome.

I don't get such a notice. It may have something to do with your settings on the Privacy & Security page in Options/Preferences. For example, in Enhanced Tracking Protection, select 'Standard'. Further down the page, do NOT select "Block dangerous and deceptive content".

I've adjusted my privacy abd Security settings to standard, but got the padlock up again for what I know is a safe email site. What is going on?

I see the padlock in the url-bar on all sites, I think. It is certainly there on this site. If you don't want to see the notice, don't click on the padlock.

The padlock is just a notice, and access to its options. Don't worry about it.