If you take a laptop (or other wifi device, such as a tablet or smart phone) into somewhere like a Wetherspoon's pub or a large Tesco or Asda, you can connect free-of-charge to their in-house wifi service. When you do so you'll be asked whether you want to designate your connection as 'home', 'work' or 'public'. Selecting 'home' allows all devices connected to the network to communicate with each other, which is almost certainly what you'd want in your own home but most definitely not what you'd want in Wetherspoon's (because fellow boozers could access your files). Selecting 'work' allows limited access between devices on the network (such as sharing a printer) but selecting 'public' tells your laptop (or whatever) that, because you're using a public network, no information should be shared with other devices. So, contrary to what you seem to be assuming, 'public' is the MOST secure connection method, NOT the least!
You can continue using the 'public' setting with total confidence. However if you need your computer to talk to other devices on the network (such as a wifi printer) you might need to change it to 'home'.
Totally separate to what I've written above, it's worth remembering that BT hubs are configured to provide TWO networks. One is available to you but the other is available to anyone else who uses BT's internet service (or who, like me, pays £6 per month to access their service). So any one of millions of BT internet customers can sit in their car outside your house and (after entering their username and password) access the 'public' signal from your router. Similarly you can do exactly the same outside millions of other houses where the occupier has BT as their internet provider. There's no risk to your privacy (or to that of any other BT user) because the 'public' networks provided by BT hubs are totally SEPARATE to those provided to the owners of those hubs.