GKE currently exposes Kubernetes UI publicly and by default is only protected by basic auth.

The UI is running as a Pod in the Kubernetes cluster with a service attached so that it is accessible from inside of the cluster. If you want to access it remotely, you can use the service proxy running in the apiserver, which means that you would authenticate with the apiserver to access the UI.

The apiserver accepts three forms of client authentication: basic auth, bearer token, and client certificate. The basic auth password should have high entropy, and is only transmitted over SSL. It is provided to make access via a browser simpler since OAuth integration does not yet exist (although you should only pass your credentials over the SSL connection if you have verified the server certificate in your web browser so that your credentials aren't stolen by a man in the middle attack).

Is there a better method for securing access to the UI?

There isn't a way to tell GKE to disable the service proxy in the master, but if an attacker had credentials, then they could access your cluster using the API and do as much harm as if they could get to the UI. So I'm not sure why you are particularly concerned with securing the UI via the service proxy vs. securing the apiserver's API endpoint.

It appears to me this should be accessed behind a secure VPN to prevent various types of attacks.

Which types of attacks are you concerned about specifically?