I am a US citizen who has been offered a post-graduate position working in London. Before I accept the offer, will UK income taxes be withheld from my salary and what rate of UK income taxes will I be paying. How are UK income taxes normally collected? I understand the US tax requirements for income earned overseas.

Yes, if you work in the United Kingdom, under the U.S.-U.K. Tax Treaty, you WILL be liable for U.K. income taxes.

I am not sure you will be liable for the national insurance that covers medical costs, but most likely you will.

Yes, the money IS withheld from your salary, just like in the United States.

The people who are offering you the job can tell you what tax rates would be, or you can Google it.