I live in the United States. My father recently passed away and I have inherited money that was held in an offshore UK account. .
I am trying to find out if I will be taxed on this?

There is NO federal inheritance tax, but there MAY be a state inheritance tax. A phone call to the state tax department should get you the required information for the state.

The UK estate taxes should be paid before you get the inheritance. No U.S. estate taxes apply because the decedent is a foreign national.