Allow and Permit
Permit is more formal.
Subject + Both words + object + infinitive
For example
They do not allow/permit people to sit in the garden.
When no object is given an ing form is used.
They do not allow/permit sitting in the garden.
If we use these sentence in passive structure
[Subject] or [Gerund (an ing)] + be + allowed/permitted + infinitive
People are not allowed/permitted to sit in the garden.
Sitting is not allowed/permitted in the garden.
The passive structure with IT is only possible with
permit.
It is not permitted to sit in the garden.
Use allow [not permit] with adverb particles
He isn’t allowed me in.