I suggested using a VPN because it is an easy way of testing whether your internet provider is the cause of the issue, not as a solution. Since you are able to connect through the VPN without any issues, it appears that your internet provider is the cause, so you will now need to discuss the issue with them. The reason some internet providers do this is that mIRC is the most widely used IRC client and as such it is the one most often used by some people to set up botnets. Another way to resolve the issue might be to connect to your IRC networks using SSL, however that will not work if your internet provider is just checking for IRC-related ports.