Am I thawing this London Broil safely?
Safely?  Yes.

Cold water thaws are fine.  It's hot or warm water thawing that's bad.

Cold running water will thaw faster than cold still water, but cold still water is okay as you basically have a giant ice cube in the water (the thing you're thawing), so the water stays at a safe temperature until you're towards the end of the thaw ... it just takes a really long time compared to thaw running water.

The only issue here would be the meat getting wet.  If it's clean water, and you don't drip it on other things it shouldn't be a problem from a safety standpoint.  It can change the quality of the food being thawed (wash away flavors, cause the food to absorb too much water), so if you're going to do it intentionally, it can be worth adding salt to brine the item being thawed.

So, from a safety standpoint, what you're doing is fine ... so long as your fridge temp is set well.