How do emergency phone calls work without a SIM?

The SIM card is used by the networks to identify who you are and they can know if you are subscribed to (ie paying for) their infrastructure. Without a SIM the phone still has all of the necessary hardware to make and receive phone calls, it just won't be able to connect to particular network. In the case of an emergency though your phone will connect to whatever network is available, not necessarily the network you are subscribed to. If you can still make emergency calls it will be to cover instances where your SIM card has stopped working properly. Just like you can also make emergency calls from the lock screen in case your phone's unlock system stops working properly.

Phone Without Sim

I'm not all that technically minded, but there will be some sort of inbuilt feature on the phone to allow people to call emergency numbers without a sim card.

I cannot vouch if it works in UK, however, as I have never had need to try. I've got a sim free phone at the moment, but I currently am not in need of emergency assistance, so I daren't try it out!

You have aerials built into your phone which gives you the right to call the emergency services for free

its just a feature just incase your sim card fails and need to call for emergency only.

Unlock the phone and it will give you the option :)