As for why someone might think they may have to do this, from Rudi Hoffman's page on non-U.S. cryonics requirements:

First and foremost, the required blood and urine sample MUST BE DRAWN IN THE UNITED STATES. Blood and urine samples CANNOT be drawn in your country and shipped to the United States. Blood and urine samples CANNOT be drawn in your country and the results shipped to the United States.

Stuart, as it turns out, has used a UK-based company, 415 Independent Financial Planners -- fortunately there's enough cryonicists in the UK that there is actually a firm here that has some expertise (see here for some info), and at least Cryonics Institute has investigated and approved UK-based life insurance as a way of funding cryo with them (same link as above for more info). I don't know for sure whether Alcor accepts UK-based insurance, but they also refer you to 415 if you're in the UK.