Talk to your office network administrator.
On your 'secure' network there is some device that is filtering network access
Either the site you're trying to access is blocked outright, or (more likely, given the error message) they're using a proxy server that is intercepting the flows, and preventing the normal SSL handshake from happening (i.e. you're trying to connect to https://some.secure.org/ and the proxy server is intercepting that request, but can't provide credentials for that site (it says "hi, I'm proxy.company.com" instead), and Safari bails since it can't be sure you're talking to who you expect to be.
Either way, it's down to the network admins at work who control this. Not much you can do about it directly.