if that system is designed to be used by the public but is secured with a password that usually means that there is a fee associated with using it. if you are unable to connect to any of these networks you'll need to locate the owner/manager of that system to subscribe.
Those are likely just private networks. The subscription style services typically are not secure. Usually, any web browser page that you try to open is redirected to their login screen. Then you pay by credit card or sometimes a direct bill to a cellphone number for access.
There is supposed to be free access in "Googlespace" in Terminal 1.
lists a bunch of access at Heathrow.
has listings, and a tool that you can use on a laptop to find listings while offline.
has listings, online and offline, and membership subscriptions that give access to some spots at Heathrow that are $0.12 per minute, and others that are included in the subscription (noted as Surf-and-Sip locations).
You might want to look at
which offers service concentrating in the UK and Europe. They are also available via a Boingo subscription, among other services.
Your cellphone provider might offer an additional subscription for WiFi spots, or you might just pay a daily rate as needed.
Is hard to find from the bt.com page, for some reason ;-( It shows up in a search.
In the US, if you have AT&T DSL, the Wifi subscription is an additional $1.99 per month.