In the first place, these days, the Crown confers honors on the advice of the Prime Minister. I suspect that if Queen Elizabeth strongly wanted somebody to get a knighthood, a decoration, or whatever, Tony Blair would put him or her on the honors list, but in the normal course of events, it's his call. If they were lobbying Buckingham Palace, as this implies they were, they were probably lobbying the wrong people, especially because...
In the second place, I'm not naive about the politics that occasionally play a part in the British honors system, but am I the only one who finds the concept of "lobbying" for a knighthood ever so slightly tacky? I have to think Blair would. I'm almost certain the people at Buck House would.
". . .but am I the only one who finds the concept of "lobbying" for a knighthood ever so slightly tacky?"
You might be, but you are really on the right track.
I, on the other hand, find it majorly, purple-and-orange
tacky for him to lobby for a knighthood.
Now I might support him if he were to lobby for a hood
ORNAMENT.