Websafe works by being able to see the traffic on your home broadband connection, and blocking those sites you've chosen to be blocked.
VPNs by design channels all traffic over a private connection - which hides what sites a device using VPN is connecting to from the network monitors.
So there is fundamental design difference between any network blocking system and a VPN.
VPNs by design can use lot of different sites, ports and connections, so they can be difficult to block using network or router tools. There are many reasons for this, from getting around censorship in some countries, getting around region content blocks for streaming services, to getting around your parents!
The only guaranteed way to stop a VPN is to stop the client being installed or the service being used in the first place.
********************************** I work for Virgin Media - but all opinions posted here are my own
AFAIK, only DNS traffic is examined and when appropriate that is short circuited to respond with an IP address that points to Virgin Media's alert / warning web pages. You need to lock down the device to stop any system changes (i.e. installing new software, connecting to new networks, changing DNS, etc) but even then vigilance and education is the best defence; hopefully more of the latter.
BTW, a VPN has much to offer so you may wish to add it in an appropriate way to enhance privacy and security.