What are the actual rules for riding e-scooters on pavements and cycle lanes in the UK?

I’m trying to understand the rules around e-scooters in the UK because I keep finding conflicting information.

As far as I understand it, privately owned e-scooters aren’t generally legal to ride on public roads or cycle lanes, while rental e-scooters are allowed in certain areas under the government trials. But then I’ve also seen people saying there are situations where riding on a cycle lane/pavement may be allowed, and that you need some form of insurance for an e-scooter to be legal.

Can anyone clarify what the actual rules are?

Specifically:

• Can you legally ride an e-scooter on a pavement?
• Can you ride one in a cycle lane?
• Does it make a difference whether it’s a privately owned scooter or a rental?
• What exactly is the insurance requirement, and who provides it?
• If private e-scooters aren’t allowed on public roads/cycle lanes, where are you actually supposed to ride them?

The whole thing seems unnecessarily confusing, especially the insurance part, so I’d appreciate it if someone who actually understands the current rules could explain it in plain English.

Cheers!