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Unfortunately, as a resident of the US for tax purposes, you are required to report (and pay tax on) your worldwide income. In the case of the rental property income, you will report and pay tax on it in the US. If you had paid tax to the UK on the rental income, you could have taken a credit for the taxes paid to the UK.
Article 6 of the Tax Treaty between the US and the UK provides that:
1. Income derived by a resident of a Contracting State from real property, including income from agriculture or forestry, situated in the other Contracting State may be taxed in that other State.
2. The provisions of paragraph 1 of this Article shall apply to income derived from the direct use, letting, or use in any other form of real property.
3. The provisions of paragraphs 1 and 2 of this Article shall also apply to the income from real property of an enterprise.
Your tax preparer is correct.
Please let me know if I can assist you further.
Thank you and best regards,