I think Browning wrote this when Wordsworth accepted the title/post of Poet Laureate in 1843, and in doing so seen as finally having publicly abandoned any remnants of his youthful radicalism.

The thing about Blair is that people feel betrayed. No one can feel betrayed by Bush - he's given people who voted for what they were voting for, even if they may not feel too happy now about how it worked out. He pretty clearly isn't someone anyone could seriously expect much good from. But with Blair people could, and people did. "I'm a pretty straight sort of guy" he famously said, asking people to trust him, and in large part they believed he was and did trust him.

Browning couldn't have written that poem about someone who he hadn't admired as a great poet, and one whose judgement he had trusted.