Indeed, recurring visits will at some point have you considered a United States resident for income tax purposes.
See Substantial Presence Test that says, in part:
You will be considered a U.S. resident for tax purposes if you meet the substantial presence test for the calendar year. To meet this test, you must be physically present in the United States on at least:
That is a substantially different result than just visiting the US as it does represent a change in residency.
There is an exception if you can show Conditions for a Closer Connection to a Foreign Country :
Even if you meet the substantial presence test, you can still be treated as a nonresident alien if you:
In summary, you will be treated as a United States resident for income tax purposes if you repeatedly spend more than one half the year in the United States.
Even if you are a United States resident that is subject to income tax on worldwide income, there may or may not be any total increased tax burden due to Foreign Tax Credit claimed on Form 1116 . In simple terms you will be allowed a credit for your taxes paid to the United Kingdom on your United States income tax return up to the amount of tax that you paid; but only at the tax rate applicable to US tax. In other words, if your income tax bracket in the United States is lower than your rate in the United Kingdom, you should not incur additional US tax; but if your rate in the US is higher you will pay US tax to the extent the US rate is higher than the UK rate. There will be the increased filing requirement and reporting burden.
You are wise to be concerned and planning for the tax implications. It would likely serve you to have a consultation with a tax practitioner experienced with UK citizens resident in the United States to apply the rule to your specific situation. You should also examine the provisions of the United Kingdom (UK) - Tax Treaty Documents as some types of income are only taxed in the country of residence.
I hope this helps for general information on when one is considered a resident for US income tax purposes.