Firebrand shadow chancellor John McDonnell has undergone a transformation in recent weeks. Whereas Jeremy Corbyn remains every inch the protester (albeit one with a bigger stage to play on) McDonnell has adapted to his new office with a professionalism that eludes his leader.

The central complaint among Labour insiders is that Corbyn just isn't very good at politics. He doesn't have the instinct necessary to perform on the national stage, or the touch required to reach into people's homes and appear as a credible Prime Minister in waiting.

He is, in short, set in his ways – and they're the ways of the lifelong protester. Corbyn appears content with his role – paying tribute to obscure playwrights, tweeting his support for niche workers' rights campaigns and joining in with anti-government protests. It's admirable, in a way. He's always addressed anti-nuclear rallies and he's not going to stop doing so just because he's now Leader of Her Majesty's Opposition.

His shadow chancellor, meanwhile, is relishing a newfound position at the top of British politics, and has shed his old skin with remarkable ease. Watching him work the Sunday morning political shows, with his sensible soundbites and moderate policies, one could almost forget that this is a man who spent much of his life as the radical outsider.

When he was appointed to the top job in Corbyn's team, his personal website still carried commitments to “fermenting the overthrow of capitalism” – including a 60p top rate of income tax and the full public ownership of the banking system. These pledges have since disappeared, to be replaced online by platitudes about building a “new economic consensus.”

Alongside this public rebranding, his political power base is expanding. McDonnell now chairs Labour's 8am daily meeting and is in charge of the policy development process. He is understood to covet Corbyn's job and is actively trying to bring the hard-left and the soft-left together, in order to make that happen.

There are even those who maintain that the entire Corbyn leadership bid was masterminded by McDonnell. So keep an eye on this die-hard socialist. He may have changed his soundbites but he's unlikely to have changed his politics.