Mark Leftly: Margaret Hodge, feared basher of bosses, may be ready to step up to a bigger stage

Westminster Outlook There she was, Margaret Hodge, blasting big business bosses, reducing them to guilty-looking schoolboys, as she has done week on week, year after year since 2010. Ever being told off for their shoddy work, G4S and Serco were back before Parliament's embodiment of a fierce, righteous headmistress this week. In fact, Serco had just returned from a suspension on winning Government contracts, having only avoided permanent expulsion after promising "corporate renewal", an irritatingly opaque phrase if ever there was one.

This time, the contractors were caned for providing sub-standard housing for asylum seekers, failing to make the grade in the first full year of a contract that is supposed to save the taxpayer £140m by 2020.

There was no way that Serco's home affairs managing director James Thorburn, or the G4S care and justice services executive Stephen Small, were leaving Wednesday's Public Accounts Committee hearing without wanting to cry.

Mrs Hodge's words alone do not fully convey her exasperated tone and manner, but you'll get the gist of what she thinks of two of Britain's biggest employers: "You do a lot of contracts. You claim expertise and experience, which is relevant to your doing this asylum seekers' accommodation. You Sign up to it. You Sign up to it. You can't then say 'actually, it's all much more complicated than we thought'."

The accompanying gestures are marvellous. There's the hammy rolling of the eyes; the chopping hand gestures; the nod, in time with every over-emphasised word; the particularly scornful snigger (usually made with a turn to her right) at oblique business language; and – in what I think is a new addition to her repertoire – a hand on her head to mock the monkey-like confusion of those put before the committee, used in this instance on the words "all much more complicated".

Heading the House of Commons' public spending watchdog is a job that Mrs Hodge absolutely loves, which cannot be said of some of her more feted predecessors. Harold Wilson was said to have chased the role just so as to snaffle the chair's oak-panelled office in the heart of the Palace of Westminster, with its breathtaking views of the River Thames.

You would think that it would be a good thing if the MP charged with making sure that every penny of state money is spent wisely in a supposed age of austerity actually relished the role. The Treasury doesn't think so. Last month, No 11 let it be known that officials believed Mrs Hodge's incessant criticisms of businesses, such as using perfectly legal tax reduction plans, is putting off foreign investment.

One Treasury source was widely reported as saying: "There is no doubt it is having an impact. We are trying to show we have one of the most competitive corporate tax regimes in the world, but the message is being sent out if you come here you will be exposed to this sort of criticism from Margaret Hodge and her committee."

Mrs Hodge thinks the most effective way of getting businesses to spend public money better is by providing "great theatre", as one committee source puts it. There seems to be resentment within government that she is undoubtedly the star of this particular show.

Whether she's more of a headmistress or a leading lady, Mrs Hodge is now, in her 70th year, certainly one of the most significant politicians in Westminster. She has been badly underestimated, once a mid-ranking minister best known for being dragged into a bitter battle with BNP leader Nick Griffin to retain her Barking seat at the last election.

Few thought she would do much with the committee. Mrs Hodge might go over the top too often and rather dramatically so – most infamously saying that she thought Google "do evil" – but what she has achieved far, far outweighs any of the negatives, quite rightly highlighting the failures of companies that are, after all, working for us.

The success of the underrated usually provokes contempt and, ultimately, bitterness from the critics who miscalculated.

Goodness knows, then, what her opponents at the Treasury will think when this grandmother 10 times over emerges as a strong candidate for the mayor of London. Mrs Hodge now has a strong public profile and the inquiries she has run – from the private sector mismanagement of the clean-up of the Sellafield nuclear facility to a forthcoming look into how the Ministry of Defence wasted millions on a failed IT system – are undoubtedly populist.

The "seed", I am told, "has been sown" in Mrs Hodge's mind about a run for the 2016 mayoral election.

There is talk that she has been inundated by unsolicited suggestions that she should take on front-runner Tessa Jowell and the likes of the brainy Lord Adonis for the Labour candidacy.

Ed Miliband's introduction of a primary system for the mayoral race will probably help Mrs Hodge's chances, as Labour supporters, not just members, will vote. That bigger electorate will know who she is and probably like the bashing both of failing contractors and of the nature of our corporate tax system. It's a big 'What if?', but Mrs Hodge's conduct on the committee does leave a major problem should she become mayor: on a daily basis, she would have to work with the same companies, which are also London's contractors, that she has publicly condemned for so long.