This could work but check with your DM
I think this works, but this is not quite as clear cut as you make it out to be.
Can you react to "starting a movement"?
First, there are no specifics what you can use as a condition, so the DM will have to weigh in on that. It seems pretty clear that the condition needs to be observable for your character to react to it. Is it observable that the opponent is "starting movement"? I personally would think this is fine, in particular as there is specific guidance about spellcasting that says:
You can ready an attack against a spellcaster with the trigger "if she starts casting a spell."
If you can react to someone starting to cast a spell, it should be possible to react to someone starting to move, too.
Must the creature carry out the movement?
Second, while it says that the creature continues its turn, it does not say it needs to carry out the turn in exactly the same way. Neither does it say it must continue its turn as you claim, it just says it continues it turn, because the turn is not done yet.
If I want to move somewhere and suddenly a prismatic wall springs up in front of me, I might consider moving somewhere else or do something else entirely instead.
So, rules as written this part does not work. If it would, then you also have to deal with opponents using it against the player characters, and it is quite obvious they would rightfully protest against that. As @Kryan's answer details, nothing in the rules would force the creature to execute its move like that.
But for a dramatic fight, I think this could mostly be fine, especially if you define it as something like "if the creature tries to rush me to attack" or something like that, but you need the DM to go along with it. For example you explicitly can Ready a Weapon against a Charge. However, there the opponent then knowingly charges you, even though you have a spear set ready to pierce them.
There is a cost to readying actions
Casting a prismatic wall offensively would be plenty powerful, and the spell specifically declares its intentions as a defensive device by stating
A prismatic wall spell cast to materialize in a space occupied by a creature is disrupted, and the spell is wasted.
However, there is a hidden cost to this tactic that makes it less powerful than it appears at first glance: to ready, you have to forgo your action, and bet on the other creature moving in on you. If the creature opts to not move at all, and instead casts a spell or uses a breath weapon on you, you just wasted your entire action.
Secondly, depending on how specific your DM wants it, you may even have to declare where exactly you will put your wall, and if they decided to move somewhere else, you have spent a high level spell slot and your action to put an otherwise useless wall onto the battlefield.
In summary, I think this can work, and it can be a cool effect if used once in a climactic battle; but since it would be pretty overpowered if it would work very reliably, and that will make the game less fun, any DM worth their salt will start to nerf this tactic pretty quickly if you want to use it repeatedly, and they have a number of legitimate tools to do so.