Square > Physical shape > Walking a square

Square –
“1. A plane figure with four equal straight sides and four
right angles.”
Mac Dictionary Definition

By definition it should be possible to walk a square if you use some measuring device to make sure the sides are of equal length and a compass to measure you are walking north, then east, south and west. In theory you should arrive back where you began.

I wondered how possible this would be in a city like London, one that has grown organically over the years, where the streets are a labyrinth. I knew the answer would be no but began thinking the shapes the streets made would be interesting and unexpected.

“...by fixing my eye on the polestar, and seeking ambitiously for a north-west passage... I came suddenly upon such knotty problems of alleys, such enigmatical entries, and such sphinx’s riddles of streets without thoroughfares... I could almost have believed, at times, that I must be the first discoverer of some of those terrae incognitae.”
Thomas De Quincey, Confessions of an English Opium Eater

Is it possible to walk a perfect square in a city?
What will happen if I try?
What will I see?
How/what will I document?
How will I measure the accuracy?