I am a UK citizen working as a Research Scholar on a J-1 Visa in the US. I am planning on staying here less than 2 years. I accepted the job offer assuming that I would be exempt from taxes because of the tax treaty. However, I was charged taxes from my first paycheck.

I have asked my university and they said that as a non-resident alien they withhold 14% taxes from my stipend. They also said that the UK doesn't have a treaty with the US that covers scholarships/fellowships. However, I think I should be eligible for the tax exemption as I feel that the tax exemption agreement does cover my situation. What is your opinion?

I agree that you are entitled to the exemption. The technical explanation for the 2001 U.S.-U.K. Tax Treaty is below, and seems pretty clear to me:

Paragraph 1 of Article 20A provides that a professor or teacher who visits one of the Contracting States for a period not exceeding two years, for the purpose of teaching or engaging in research at a university, college, or other recognized educational institution in that Contracting State, and who is immediately before that visit a resident of the other Contracting State, will be exempted from tax by the first-mentioned Contracting State on any remuneration for such teaching or research for a period not exceeding two years from the date he first visits that State for the purpose of teaching or engaging in research. Since this two year period is determined from the date he first visits the Contracting State, periodic vacations outside the first-mentioned Contracting State, or a brief return to the other Contracting State will not toll the running of the two year period. Like the existing Convention, if the two-year period beginning from the date of his arrival is exceeded, the exemption will be lost retroactively. Thus, if a person comes to a Contracting State for the purpose of teaching and stays for a period in excess of two years, the exemption will not apply for the first two years.

Since your university insists on withholding the tax, you just need to file Form 1040NR-EZ (and Form 8843) and claim the exemption to get a complete refund.

Note that the STATE where you work and live may or may NOT honor the treaty; a phone call to the state tax department can get an answer to that question.

Thanks for your answer. When you say I need to file the forms and claim a refund, is that something I can only do at the end of the tax year? Obviously it would be nice to get all the money back, but it would be difficult to have enough money to live on throughout the year while they are taking the tax, and so it would be better if I can get them to stop withholding it now. Is there any way to do this?

The only way is to convince your employer that you are exempt from taxes so they stop withholding.