Check if you have some proxy or stateful firewall enabled
It is also possible that split-tunneling is not enabled, or that the routing does not permit you to use the same internet gateway on the VPN network that other local users can use. This is a typical security measure.
Alessandro is right, it depends on the security measures implemented. I can get on the internet while on my company’s VPN, but I am subject to the same site restrictions as I am when I am at work on the intranet there.
What is your VPN make and model. There are a lot of features that will fix this; i.e URL rewriting, split-tunneling, Access Lists, etc. Just depends on how you want it setup.