When I log into my emails the padlock icon at the top of the page goes off and it informs me that the site is not secure. This also happens if my wife logs into her emails. We are both using blueyonder addresses.
Seriously - there's nothing wrong with the site the issue is with the pictures in the emails.
Many senders don't send the picture itself in the email. Rather you get a link to a picture which the mail client (in this case your web browser) then connects to the online resource and shows the picture.
In either case the main body of the mail is sent securely, but the pictures can be sent securely via HTTPS or insecurely via HTTP meaning you end up with a mixture of secure email content which eavesdroppers can't see and insecure pictures which can be seen and possibly modified.
It is this mixed content that causes the whole mail site to be shown as insecure. Once this happens then unless you refresh the whole page, the insecure warning stays up.
If all email senders were to use HTTPS links for their images then the issue wouldn't occur.
Looking at mails using webmail I found
The Register uses HTTPS for it's images - meaning the mail site stays showing secure when I show pictures The Telegraph uses HTTP for it's images - meaning the mail site ends up showing insecure when I show pictures.
It's one of these features that is meant to help users but IMHO can end up doing more harm than good.
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