Am I the only one who, on reading the headline, can't get out of their head the sound of The Police and Sting's voice?
"Every move your make
Every breath you take
I'll be watching you"

From the last line of the article (yes I actually read it)
"This can be important when it comes to faulty lines with bad (or even disconnected) joints still providing some level of broadband service.”

I can attest to this. My phone line broke, or at least one of the pair of wires did, about 100 yards from my house (according to the TDR readings taken by the BT engineer that came to fix it). I still retained about 7Mbps down and 1MBPs up but could not make landline phone calls. My normal speeds normally hit whatever limit they put on my connection, which at the time was 40Mbps down and 8Mbps up.

Not sure which "they" you mean -
TfL? they have no access to the wifi data outside of their physical infrastructure. If you are unclear about what that is then perhaps you might want to reflect on one of the names the system is known by, the underground. The wifi signals will not reach into retail premises unless they are within the station.
You could of course be referring to the company that is contracted to provide the wifi service (is this still O2? I can't be bothered to look it up) but then it relies on the retail, or other premises, using the same provider.

There is always the option that other people have mentioned. Turn off your wifi - properly. Aircraft mode and the power button are 2 options that spring to mind.
In addition to this one can always take the position of someone I was speaking to yesterday - they have a basic phone, no mobile data, no wifi, no email, self contained calendar. Photos extracted by USB cable. Now in their case this is a deliberate step away from technology rather than trying to be anonymous but if you really want to be anonymous why carry something that relies on being consistently identifiable during operation by non-physical contact means?

Living in London...
and yet...
Can't get anything from Virgin Media except via my BT phone line.
I am surrounded by areas that have cable access and yet it is not available here, and every time I check there are never any plans to install it.
Just waiting for BT infinity to become available. This keeps slipping but at least I can be confident it will happen this decade.