Drones still send and receive data from the controller in autonomous modes (the user couldn't cancel the flight otherwise) so they probably still can.

You can build your drone to do whatever you want, including continuing the flight if signal is lost. It's all open source software anyway, and cheaper than a closed-source DJI or whatever.

Not necessarily. Plus drones can easily be controlled over cellular internet.

I don't know about the UK, but where I am it's easy to get a 4G SIM preloaded with data using bogus personal information.

You don't need any personal data in the UK. They're 50p in the shops. You do need to activate them with an over the counter top up though. They accept cash.