I am not finished, let me speak on.

[Odessa Dawn]

While you are speaking and others interrupting you, you could say I am not finished, let me speak on, couldn’t you?

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[5jj]

It's not very natural. Try:

Hang/hold on. I haven't finished what I was saying.
Do you mind letting me finish what I'm saying?
Let me finish (what I'm saying.

 

[Tdol]

Or just I'm (still) talking.

 

[Barb_D]

How you say it will depend a lot on your relationship with the person who interrupted you. If my kids interrupt me, I may say something different than if my boss does. It will also depend if others are present and you don't want to make the person who interrupted you look bad, or come across as a total jerk yourself.

There are also a wealth of sarcastic responses.

 

[5jj]

There are also a wealth of sarcastic responses.

Pardon me for speaking while you're interrupting.