Remember that under the UK's parliamentary system, the majority in Parliament selects the PM in the first place. They select him and they can remove him by a vote of "no confidence". Unlike the US system where the people elect (albeit indirectly via the electoral college) the President. The founders of the US felt that splitting power to declare war from that to make war, between Congress and the President, was wise, but in the UK Parliament has in effect both legislative and executive power.
In a way, this shift would change little.
You may be right but I think Brown's recent proclamations about Islamic TERRORISTS, the WOT & his war power giveaways doesn't inspire confidence in our once staunch ally.