Increasing the penalties if caught using a phone while driving will only be effective as a deterrent if people see that detection and prosecution rates rise.
I don't think that's true. I think the risk of the bad thing happening (getting caught) and the consequences if it does happen (the punishment) can be balanced against each other.
As an example, imagine crossing stepping stones in a shallow stream. Youl'll cross because if you fall off, you'll get your feet wet. No big deal. Now imagine the same stepping stones with a 100 foot drop all around. You probably wouldn't choose to cross those. The risk is the same: the consequences if the risk is realised are hugely different, and that affects your decision as to whether to take the risk.
Coming back to driving, the reality is that you're very unlikely to be caught for any driving offence. And short of hugely increasing policing (pretty unlikely just now) that's not going to change.
If you are caught, punishments are mostly wrist-slaps. Three points and £60? It's monopoly money. If you can afford to run a car, £60 is a pinprick.
Let's make those punishments hurt: let's impound cars and impose short-term driving bans. That would make people realise how much they value their cars and being able to drive - and reinforce the idea that driving is a privilidge that can be taken a way, not a God-given right.
If we did this, it wouldn't be long before everyone knew of someone who'd been banned for a week or a month for speeding or using the phone while driving. For those whose cars are part of their status, that would be embarassing. For those who depend on their cars it would be a real punishment, making life difficult. (Should have thought of that before they committed the offence). Word would get around that it wasn't worth the risk.
So, if we can't improve the chances of numpties getting caught, we can prevent them committing offences in the first place by making the consequences if they are caught sufficiently unpleasant.