A character who is gagged or in an area of silence can not use Verbal components
PHB pg. 203, Components:
Most spells require the chanting of mystic words. The
words themselves aren’t the source of the spell’s power;
rather, the particular combination of sounds, with
specific pitch and resonance, sets the threads of magic
in motion. Thus, a character who is gagged or in an area
of silence, such as one created by the silence spell, can’t
cast a spell with a verbal component.
Being underwater effectively gags your character, and even if that wasn't enough, the requirement to create specific pitch and resonance would effectively eliminate your verbal casting ability.
As for being effectively gagged: There is no provision for what constitutes being gagged in D&D 5e. Since it uses plain english definitions, gagged as a verb means you are blocked, stifled, muffled, smothered, stopped up, etc. Water would serve effectively to do this.
If your domain or racial features allow you to speak normally while underwater, it would obviously bypass this restriction. Breathing normally isn't the same thing as speaking normally however, just to caution you.