Both are possible. ‘Allow’ is an action verb, so it can used any tense form. Depending on the context, the present continuous (I am allowing …) can work better; as:
(Conversation between an employee and boss)
Employee: Sir, there is a family function at home. I would like to go [STRIKE]out[/STRIKE] now and I'll return within an hour.
Boss: Ok, [STRIKE]just now[/STRIKE] I'll let you go, but make [STRIKE]it[/STRIKE] a point [STRIKE]to[/STRIKE] of coming back and finishing the assignment given to you.
Both are indeed possible, and there is another alternative:
I'm letting you go outside.
Parent: I'm letting you go and play outside, but don't be long.
Child: OK, I'll be back in half an hour.
In the example given above about the family function, I don't think that the present continuous would be used. If you ask permission to leave work, I think you would be more likely to be told "OK, I'll let you leave".