I think I get what your question is... Not sure though!!!
Question: When do you have to worry about PAYING tax, as opposed to FILING tax?
Answer: You have to file if your income is over the standard deduction combined with one exemption. But paying tax is another matter.
When your income from wages and other things (including child benefit, employer pension contributions, interest, dividends, PFICs, etc.) is greater than the combined total of:
(a) wages over $82,500 (indexed annually for inflation so bigger next year)
(b) your standard deduction (or itemized deduction if this is greater)
(c) your exemptions.
If you are over this amount, which alas varies from person to person, then you *may* have US tax. Most people have enough UK tax to offset the US tax, leaving them with little or no tax to pay. Usually what will end up triggering tax will be large amounts of UK-tax-free income, so that there won't be enough UK tax to offset the US tax. Typical sources of UK tax free income include ISAs, pension contributions, redundancy pay, certain lump sum pension payouts, and the sale of a primary residence.
In short, you may never pay US tax return in the entire time you are here.