How independent is Britain's nuclear deterrent?

If Britain ever decides to press the red button, will the americans allow it to go ahead?
Since it's their technology do they not get the last say on how it is used? One of the several foreign policy mistakes made by the British leaders of the 1950's and 1960's was to think that Britain could obtain nuclear power status on a shoestring: but you only get what you pay for. While France spent more money and took longer to develop a nuclear arsenal, at least theirs is fully independent. Britain placed itself under the american system, and has since paid the price in reduced sovereignty.

http://www.danplesch.net/articles/6-WMD-Report.html

http://www.newstatesman.com/200603270008