Your short answer is yes, you do need to "report" your United Kingdom income, whatever that amount is; however you may not have to pay United States income taxes on it. A complete answer to your question is somewhat longer, so please continue reading.
Please also note from the outset that this answer addresses your income tax questions from the point of view of United States compliance requirements; it does not touch on United Kingdom tax compliance matters. Presumably, though, as you are now living and working in the UK, you've begun to be taxed under the UK system, which, if we may make an observation, is generally considered to be somewhat easier to navigate than the US tax code.
To begin, all United States citizens,
even those continuously living and working abroad for years, must file USA
income tax returns to report their worldwide income. The good news for you is that,
living overseas (and if working for a private, non-government employer, or being self-employed), provides
you with opportunities for some significant tax benefits, which you can take by
completing Form 2555 and including it with each year's tax return (Form
1040, for USA citizens).
Form 2555 (Foreign Earned
Income Exclusion) calculates the amount of foreign earned income and / or
foreign housing that you can exclude from US taxation; the limits are quite
generous and generally increase year over year.
In order to take advantage of Form 2555, you must satisfy both the "Bona Fide Residence Test" and the "Physical Presence Test." The IRS rules for these tests are explained on Pages 1 through 3 of the Form 2555 instructions, which can be read here:
https://www.irs.gov/pub/irs-pdf/i2555.pdf
In addition, this IRS.gov webpage has additional examples on meeting the 330 days required under the Physical Presence Test:
https://www.irs.gov/individuals/international-taxpayers/foreign-earned-income-exclusion-physical-pre...
Now then, assuming that you own a
bank account or maintain other financial assets in a foreign country (that includes the UK as well as elsewhere), there are certain foreign financial
account reporting requirements that you must meet annually, in addition to
filing a primary tax return (Form 1040, etc.)
In fact, there are two
separate disclosure forms that may be required; each also has different
reporting rules. One is known as IRS Form 8938, and can be
attached to the relevant yearly Form 1040 tax return. The other is FinCen
Form 114, which can only be filed via the internet. The following
Internal Revenue Service webpage describes them in some detail, and provides
their dollar value reporting levels:
https://www.irs.gov/businesses/comparison-of-form-8938-and-fbar-requirements
Form 8938 is included in
TurboTax; FinCen Form 114 is not, and you may need to access that reporting
webpage separately, if your foreign financial assets total over the
limit(s). Note that you can get to the FinCen reporting internet site
through the above IRS link.
In conclusion, the answer to your original question is that you must "report" your UK income on your US tax return, but you may well be able to escape US taxation on it, in whole, or in large part. There are also overseas financial account reporting requirements to be met, as are detailed above.
Thank you for asking this important question.
