What the treaty does, and what it does not
Think of the treaty as a rulebook that decides who taxes what, and who has to give credit for the other's tax. It allocates taxing rights for each category of income, caps withholding at source (portfolio dividends at 15% under Article 10, interest generally taxable only in your country of residence under Article 11), and provides the credit relief in Article 24 that prevents full double taxation. What it does not do matters just as much: it does not stop you filing in either country, it does not replace each country's domestic residence rules, and it does not touch US information reporting such as the FBAR or FATCA Form 8938. Under Article 17(3), US Social Security paid to a UK resident is taxable only in the UK, one of the clearest individual wins in the agreement, and our guide to double tax relief covers how the credit mechanics operate more generally.
The tie-breaker and the saving clause
If you are resident in both countries under their own rules, Article 4(4) assigns you to one country for treaty purposes through a cascade: permanent home, then centre of vital interests, then habitual abode, then nationality, then mutual agreement between the authorities. You settle UK residence first under the Statutory Residence Test before the tie-breaker is ever reached. For Americans, the biggest limit is the saving clause in Article 1(4), which lets the US tax its citizens as if the treaty had never come into effect, so winning the tie-breaker does not stop the IRS. The fix is the credit system: Article 24(6) re-sources certain US-source income as UK-source so the UK tax you pay can be credited on US Form 1116, which is what stops the same income being taxed twice in full.
Claiming treaty benefits in practice
There is no single form that turns the whole treaty on. A UK resident cuts the default 30% US withholding on dividends to 15% by giving Form W-8BEN to the US payer or broker; credit relief is claimed on Form 1116 on the US side and through the foreign pages of the Self Assessment return on the UK side; and a treaty position that overrides US domestic law is disclosed on Form 8833, where the penalty for non-disclosure is $1,000 per failure for individuals. Some questions are genuinely unsettled, most notably the US treatment of the UK 25% tax-free pension lump sum, so do not assume a benefit applies until it has been checked against the wording. Horizon coordinates the UK side, including residence, Self Assessment and foreign tax credit relief, on fixed fees agreed upfront, and a free clarity call at /book is the easiest place to start.