If your workplace has blocked the ports necessary for using IRC I recommend you talk to the network administrator or equivalent and get help accessing it. If mIRC doesn't work I doubt a web browser client of some sort is likely to have anymore luck.
If your workplace has barred IRC we respect that decision as we have no idea who you are or what your work entails and how irresponsible we'd be for helping you get on to IRC. Nor do we have a way to clarify anything you tell us!
We can't really help you anyway due to the fact it's more likely to be how the network is set up and firewalls/routers etc. rather than an mIRC issue. So really, the person who is in charge of all that stuff is more likely to be able to assist.