The sentiment is nice, but the process you suggest is wholy undemocratic and no different in principle than what we're protesting. What can bring Blair down is a vote of no confidence in Parliament; so, exerting pressure on MPs to do so is where that effort can escalate since, as the Mirror notes, some already have that notion.

The aussie prime minister that was 'dismissed' by the queen was in fact removed eventually in a cia backed campaign because of his left wing anti veitnam stance, and not by the queen either, but by her 'representative' the gov. general.
If we need to rely on those sniverling cowards in parliment or the richest woman in britain and distant relation to king george, then we really are in trouble.
Better to do it for ourselves with imaginative acts of civil disobendiance. These can range from blockades, not going to work, sabotage, repeated, ridiculous and absurd use of beaurocracy (requesting forms filling them in wrong and sending them to the wrong department and then complaining loudly that the process has malfunctioned etc etc - checks stapled through the middle ensure a slow down of bank systems, especially if they are for a few pence - post more ideas here)
In the words of my fav. graffitti; be your own leader you feeble burke.
I dissent.