The market as an institution is 850 years old; the building that currently houses that institution is 42 years old. The market is not a place; it is the activity in which people engage in that place.
And no laws or legislation have been passed or proposed to close down said institution, is that accurate?
As far as I'm aware they do need an act of parliment to close it down. The one to create the market on the current site is an Act of Parliament (The Metropolitan Meat and Poultry Market Act of 1860) which should protect the site from becoming anything but a place to provide Meat & Poultry
They are in the process of absolving their legal obligation to continue operating the market.
So the market moved 40ish years ago, and now it has to move again, the institution is fine?
No, if you read the article, the City of London is washing its hands of having to relocate the institution at all.