Gfyuki

From the Basic Rules section on Concentration:

Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends.

If a spell must be maintained with concentration, that fact appears in its Duration entry, and the spell specifies how long you can concentrate on it. You can end concentration at any time (no action required).

The rule is very short and only says "at any time (no action required)". How this "any time" is defined?

An example scenario:

I cast levitate on an enemy to remove them from the battle. Later at his turn, it turns out that he brings a crossbow. The DM declares the attack, but then I interrupt him and say that I end my concentration, so he will fall down and become prone.

Another example scenario:

I cast levitate on myself and fly 30 ft. The enemy then flies and spends all his movement to fly to me to attack me in melee. After he reaches me, I declare ending my concentration, so I can fall back to the ground, preventing him to attack me.

Is this allowed? Can I end concentration conveniently any time, interrupting any currently declared action/event?

You can end concentration at any time (no action required).

As it says above, you can end it at any time, no action required. It means you don't need to use a reaction, so you can elect to just end it.

Which means yes, you can end your concentration as an enemy approaches so that you drop out of their reach.

To act on another character's turn usually takes a Reaction

You need to discuss with your DM whether or not, absent a game feature that offers you a Reaction, you can by default interrupt any currently declared action/event to stop concentrating at any given time, or if you must wait to stop it when it is your turn.

• For case 2, if as the flying creature approaches you he sees you
  dropping, would he not adjust his course to try intercept you?


• 
  

  And for case 1, how does the DM determine if he got off that shot
  before you stopped concentrating? Dex check? Int check? An advocate for that character could argue that they loosed the shot "at the apex" before they you noticed them and chose to stop concentration.

  
  
  

  It might seem to a given DM that you are manipulating the turn system mechanics to provide a mini-time stop that allows you to interrupt their turn. Discuss with your DM.

  
  

Certain special abilities, spells, and situations allow you to take a
special action called a reaction. A reaction is an instant response to
a trigger of some kind, which can occur on your turn or on someone
else’s. (Basic Rules, p. 73)

Since neither of those spells explicitly has that provision, this requires a DM ruling in terms of timing.

Arguments for the interruption

Since your concentration can be broken on another character's turn (when damage is done to you) you can reasonably argue that dropping concentration on another's turn is consistent with that, since

You can end concentration at any time (no action required).

Lino's answer is a valid ruling, as would be an answer that requires that you only act on your turn unless you have a reaction that allows you to act on another character's turn. Dropping concentration then (only on your turn) would not consume your action - you would still take an action of some sort - but you'd need to wait until your turn to declare that you are dropping concentration.

Whose turn is it anyway?

During a round, each character has a turn.

The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative. Once everyone has taken a turn, the fight continues to the next round if neither side has defeated the other. (Basic Rules, p. 72)

OK, when it is someone else's turn ... what happens?

Your Turn

On your turn, you can move a distance up to your speed and take one action. You decide whether to move first or take your action first. Your speed—sometimes called your walking speed—is noted on your character sheet. The most common actions you can take are described in the “Actions in Combat” section later in this chapter. Many class features and other abilities provide additional options for your action.

Since the text on concentration does not require an action (small a) to drop concentration, then parsing that text literally supports Lino's answer: you aren't using an action, so "any time" can be interpreted as "any time, to include when some other character is taking an action within that six second round."

But it's all "happening at once" during a round

A DM can also rule that you only get to declare what you are doing when it is your turn. Interrupting others (even NPCs and monsters) on their turn is not consistent with this being a turn-based game. Waiting for your turn is consistent with D&D 5e being a turn-based game, with the exception - Reaction - being when you can interrupt another character's turn.

• 
  

  How often will you be happy to see the Monsters interrupt your turn?
  When playing a turn-based game, how often do you want others to
  interrupt you during your turn? And for that matter if, as the flying
  creature approaches you he and sees you dropping, would he not adjust his
  course to try intercept you? It doesn't take an action for him to see your location begin to change, does it?

  
  
  

  Discuss this with your DM and get a ruling. Hopefully, for your idea to work, the GM will see it Lino's way. If not, then wait for your turn and do/declare stuff then.