Usually public wifi is typically free to use.
In the UK some wifi hotspot connections such as BT however are not free unless you are a customer using their home Broadband but a person is pre warned in advance before connecting.
Also some public wifi connections require you to sign up to their terms and conditions.
Coffee shops etc offer free wifi to entice people in 
The short answer is Yes most public wifi connection is free.
Just turn Off your Mobile Data so you don't get any accidental data connection if the wifi connection drops, and don't use public wifi for private surfing such as internet banking etc.
Public wifi generally can be slower too.
I hope that helps @JobieB
