These verbs all have the same meaning. The difference is in their grammatical structure:
LET + PERSON/THING + VERB (base form – without “to”)
The simple past tense of let is also let; there is no change!
The verbs allow and permit are more formal ways to say “let.” However, with allow and permit, we use to + verb:
Permit is the most formal, let is the least formal, and allow is in the middle.
With permit and allow, we can also say that something is or is not permitted/allowed: