Certificate problem in Outlook/hotmail

I have a 'hotmail.co.uk'address which I retained when Hotmail shifted to Outlook. When the search comes up in the address bar it says something about 'dub livemail'. I have had no problems at all with accessing or sending mail. Then, yesterday I suddenly start getting a message saying there is a problem with the site's certificate not being issued by a trusted authority and that it may be fraudulent. I usually access my account via a link in my favourites bar. I thought perhaps something had happened to the link, so tried to go direct to the Outlook log in page. I get the same message appearing when I click on the Outlook log in. I read around this in Google and noted the problem may be related to incorrect date/ time settings on my computer. However,these seem to be accurate . I can access live mail OK but not Outlook/hotmail. I don't think there is a security issue as I have up to date securitysettings and scans are not showing any issues. I am a senior person and any simplistic advice would be welcomed. I don't want to press the 'ignore and proceed to site 'button re the certificate, as I am frightened what nasties I might be allowing.
Please any advice?

Hi , Thanks for the reply. I checked time OK last evening before going off to bed. I also checked on the Outlook site which was showing no problems. However, the site 'downdetectors' showed quite a few people were having the same problem I was experiencing. This morning all is back up and running which would suggest there was a Microsoft issue . Thanks fo the help though!
Tiffany