A VPN is an encrypted tunnel. All the ISP can see is a connection to the VPN endpoint. Anything you then browse to is “inside the tunnel,” when you pop out of the other end you’re past your ISP’s systems. They can’t even tell what sort of traffic it is* (web, torrents, Spotify) let alone where it’s going.
The only way what the OP describes can be possible (assuming that the VPN is actually up and working) is if it’s what’s called “split tunnel” – some traffic is going over the VPN and some isn’t. For example, if I VPN into work from home, all network traffic bound for work goes through the tunnel, but non-work Internet traffic goes out directly over my Internet connection outside of the tunnel as normal. If I change the client setting to “fixed tunnel” then all traffic goes over the VPN – Internet traffic will go through the VPN, through my company’s internal network, and out of work’s Internet connection just like if I was sat in the office. For work purposes split tunnel is desirable, but for the purposes of stopping Big Brother from spying on you you need a fixed tunnel.
The fact that this works means that the whole Snooper’s Charter business is a nonsense. The people being logged by ISPs are regular users, the criminals can trivially hide their tracks and circumvent the whole thing. Whether or not this was legislation brought about by incompetent politicians who don’t understand how the Internet works, or whether it was the intention to spy on the populace all along under the guise of being an anti-terrorist measure, I’ll leave as an exercise for the reader.
(* – note to techies, I know this is a slight oversimplification, I’m talking about for most practical purposes.)