If you are dual resident have you looked at Article 4 of the Treaty to determine where you are treaty resident should you wish to elect that?
Incidentally for UK income tax purposes no-one is US domiciled; one needs to demonstrate domicile in a specific State.
I have looked at article 4 of the treaty which is why I pose the question. We are thinking of renting an apartment year round in the UK, using it about 6 months a year. We will maintain our permanent home in the USA, and have lived there some 26 years. Both our adult children live in the US and virtually all our income (from pensions and withdrawals from retirement savings) is in the USA. From the treaty it appears that we can claim that the US is our domicile as that is where our vital interests lie.
From article 4 of the treaty,
"4. Where by reason of the provisions of paragraph 1 of this Article, an individual is a resident of both Contracting States, then his status shall be determined as follows:
(a) he shall be deemed to be a resident only of the State in which he has a permanent home available to him; if he has a permanent home available to him in both States, he shall be deemed to be a resident only of the State with which his personal and economic relations are closer (centre of vital interests);"