Whether a resident or citizen of the United States or a nonresident alien for US income tax purposes there is not any income tax unless and until there is a distribution of income (not corpus) to the beneficiary. Tax on income not distributed is paid by the trust and that is then part of the corpus that can be distributed tax free to the beneficiary according to the terms of the trust.
Non U.S. persons are subject to U.S. income tax only on their U.S. source income and on income effectively connected with a trade or business in the US.
U.S. source income for income tax purposes generally includes (I.R.C. § 871(a)):
- Dividends from U.S. corporations, but not the proceeds of sale of U.S. securities.
- Rent from U.S. real property, and capital gains on the sale of U.S. real property or real property holding companies.
- Interest on debts of U.S. obligors. However, interest on most publicly traded bonds issued after July 18, 1984 constitutes "portfolio interest" and therefore qualifies for the portfolio exemption and is not taxed as U.S. source income (I.R.C. § 871(h)).
- Salaries paid by U.S. and non-U.S. entities for services performed by the recipient in the United States.
- U.S. royalties.
Since income tax must be paid it may need to be withheld on payments of interest(except bank deposits), dividends, and other fixed or determinable annual or periodic (FDAP) U.S.-source income paid to foreign persons. The trust is required to determine and withhold as well as to get Form W8-BEN or similar from the beneficiary.
For withholding rules see Publications/TaxAdviser/2012/december/PublishingImages/mcnamara-exh1.png
For more on W8-BEN see https://www.schwab.com/public/schwab-uk-en/investing_in_the_us/us_tax_info
For more on FDAP see http://www.irs.gov/publications/p519/ch04.html#en_US_2012_publink1000222345
Federal estate tax is the responsibility of the estate and not the beneficiary. There is no federal inheritance tax due from the beneficiary.
Tax treaties influence the general rules and the required rate of tax:
"The treaty allows both the US and the UK to tax dividends paid to a resident of the other country but, subject to certain conditions, limits the tax the source country may impose to 5% or 15% of the gross amount of the dividend."
You will be subject to 15% rather than 30% rate on dividends under the treaty.
These answers presume that this is a domestic trust in the US and not a foreign trust. That is, the trust is subject to rule of US courts and control of the trust is by US persons. For details see http://www.law.cornell.edu/cfr/text/26/301.7701-7
Please ask if you need more discussion or clarification.