Technology cannot do certain things
There are certain things that GPS can't do. Sadly for the government, track cars reliably enough for taxation is one of them. Sadly for us, this won't even register as an objection. Even perfect biometrics for ID cards can only tie a person to a document, they can make precisely zero claim for the veracity of the information linked to that document. A simple case of can't work, won't work, implemented anyway.
GPS needs a clear view of the sky, without it the position can jump markedly especially with cheaper GPS receivers. I've seen a GPS fix shift 400 yards across a river and back in a steep sided valley in a matter of seconds. That kind of error would result in at least a speeding fine or charging for being on a road I was nowhere near.
Tunnels pose an interesting problem too. Total signal blackout can cause a GPS to believe it has stopped and often not reacquire position on exiting the tunnel. I have to reset my GPS manually on the rare occasions I use the Dartford crossing tunnel. I can't see people doing that if they're going to be charged for it but I can see the government sending rescue teams into the tunnel to find all the people who went in and never came out...
It's also not just malicious interference that affects GPS, sunspots also impact accuracy. Not hugely but enough to get you charged for being 100ft away on the high toll road instead of the low toll one you're on.
Fuel duty is the only meaningful way of taxing mileage, it's extortionately high now and will get worse. Even with some meaningful investment is made in public transport, governments need to accept that frequently there is no alternative to driving at all let alone a viable one.