What have the iranians got that could find a submerged Vanguard? im not talking about floating one in and leaving it anchored for all to see, but if it is spotted at some point surfacing in the region it would make the inbreds severely uneasy.
If it's in the Shatt al Arab - like you said - it would be aground. The Shatt al Arab is the strait between Iran and Iraq, leading up towards Basra. It is also very narrow and very shallow - anything submerged in it would likely be visible from the air.
If it was spotted inside the Gulf, they would find it VERY easy to block the strait of Hormuz to submarines with mines and trap it in the Gulf. The Persian Gulf is after all pretty frikking small and very close to Iran. There is no way on earth that any sane government would countenance risking a ballistic missile submarine in there - and given the fact that it's missiles can hit anywhere Iran from UK territorial waters with ease, the Iranians wouldn't be any more intimidated than they already are. The people who would be most bothered are UK Taxpayers (due to the apparent insanity of their government) and the various Arab countries around the Gulf.
All that is necessary for the triumph of New Labour is for good men to say nothing whilst CGS.