"It turned out the "key" worked great and lifted the cover right off ... And there's not much room down there to get a wrench to close the valve."

Forget the wrench. Get what is called a Curb Key or Water Meter Key. About $12 at HD or Lowes. There are fancier ones, but a plain one works just fine. Turn it gently, don't rip the valve off.

Keep that muddy area cleaned out, and keep the weeds, ground cover and ivy cleaned away from it.

Sue