I'm a Us citizen, UK resident, receive US social security and a UK state pension. I tried to figure all this out myself also but gave up and got a tax professional. If you opt to take the treaty position, you have to file form 8833 "treaty-based return Position Disclosure'. On my 2010 US tax return, on that form, here's what he wrote: "Social Security Pensions: the taxpayer is resident in the UK and taxed on a worldwide basis. Article 17 provides that the country of residence … is given the sole right of taxation. This provision is not subject to the saving clause in article 1. Therefore the US SS pension of $xxx and the UK SS pension of $... are taxed in the UK and not in the US."
As I understand it also (and could be woring) for US social security you don't have to take a treaty position. You could just, eg, declare your US social security on your US return, pay the tax, and then take a tax credit on your UK return. And vice versa (thus avoiding double taxation). Given that the tax years are different and overlapping, this is incredibly complicated. HMRC told me just to prorate it. IRS told me something incomprehensible.
Also, HMRC does know about the treaty and the US taxation. When you call the general HMRC number you ask to speak to an International Treaty specialist and they call you back. I would say that they are as helpful as the IRS people in Philadelphia. When you ask a question that they can't answer they tell you to write it up and send it to your tax office and you'll receive an answer. Or they tell you that you can just leave it on your return and they'll figure out how much tax you owe.
Bear in mind also that as a UK resident you won't have any witholding taken from your US social security so you will have to pay estimated UK tax.
It's all of course outrageous beyond words.