It'd be true if the shares was purchased on the London Stock Exchange, but AFAIK BP also trades in New York, shares in $.
Plus if it's UK shares and you get paid in £'s then read this:
http://www.hmrc.gov.uk/taxon/uk.htmThey call witholding differently, they call it "tax credit". It's 10% up to $34,800, 32.5% over that. So for example, if you are a UK tax payer and have enough income so that you're in the 40% tax bracket and you receive a dividend of $1000, $100 has already been witheld, you'll have to pay HM Revenue another $300 for tax.
As far as the IRS goes... they treat it as income, I'd guess... you'd be able to claim that 10% back from US government... Looking on IRS site, Form 1116 would be what you need to fill out. Plus BP might give a 1099-Div to make it easier too... but if they send you the UK paperwork, it'll detail the "tax credit" on that too (tax credit==tax you paid).
Disclaimer: I am not a tax professional, not an accountant, not a lawyer. I just read the appropriate sites and this is my interpretation.
Mark.