It’s been nine months since Jeremy Vine inherited the Sunday lunchtime small screen political joust from John Humphrys. All the undignified caterwauling from certain media circles that accompanied the demise of On The Record ultimately proved insubstantial enough to resolve into a disabling assault on the evolution of the BBC’s Westminster coverage. Instead, opposition seemed to just dissolve into a series of petty grudges, ending up mingled with all the non-specific anti-Beeb rhetoric that continues to be trotted out by bitter ex-employees and jealous industry rivals on a weekly basis.

While it’s true The Politics Show hasn’t generated the sort of Monday morning broadsheet headlines its predecessor used to count upon as justification for its continued existence, this is no bad thing. Sundays are already choked up with enough self-conscious “heavyweight” efforts fighting the kind of publicity battles Weekend World lost 20 years ago. In ditching, as promised, the set piece extended interview in exchange for a looser, livelier format, The Politics Show has succeeded in unshackling mainstream political television from the suffocating logic that dictated its place in the schedules was dependant upon the promotion of indigestible tracts of dogmatic analysis over and above anything that could be seen as populist or, heaven forbid, entertaining.

Besides, Breakfast With Frost, still the accepted benchmark for ponderous and protracted one-on-one interrogations, goes off air a scant two hours before Vine and his team make their entrance. The Politics Show has already made a case for brevity and energy in the packaging of current affairs, and has done so without undue recourse to overt, self-conscious displays of being “different”. The same can’t really be said of its weekday stable mate The Daily Politics, a candidate for the worst-named programme in recent memory, with an over-enthusiastic Andrew Neil promoting unsubtle “alternative” sideways-looks-at politics in an unlikeable for-the-sake-of-it manner. In contrast, Jeremy Vine just gets on with the business of presenting, never calling undue attention to unconventional items or topics, and never once presuming the absence of a set-piece interview needs compensating for with laboured jokes or swaggering bluster.

It was with just such a studiously downplayed demeanour that Vine kicked off this particular edition, offering up by way of an introduction the observation that, “Magician David Blaine today emerges after spending 44 days in a confined area doing nothing. He says he’s giving up because he’s worried he was never going to beat Betsy Duncan Smith’s record.” Not devastating satire, to be sure, but nonetheless a brisk, whimsical opening salvo a world away from Frost’s curmudgeonly japes or the traditionally arch or melodramatic tone of the Sunday debate (an hour later Jonathan Dimbleby was to be found rattling on about Tony Blair needing GM foods “like a hole in the head”).

Seated within a spacious, light blue studio, with an unobtrusive provincial skyline curving behind him, Vine exuded an air of calm authority. The lead feature, a piece on Iain Duncan Smith, opened with our host describing the Tory leader as beset by “more plots than the average council allotment.” A montage of illustrative clips included shots of journalist Michael Crick striding purposefully along a high street, though as Vine didn’t mention the man’s name it was clearly presumed viewers both knew who Crick was and what he was doing.

Vine then held brief interviews with Tory MP Crispin Blunt, last seen on TV sets stirring up trouble during council election night in May, and Lord Strathclyde, the Conservative leader in the House of Lords. These were done separately, with the pair sitting on opposite sides of the studio, and while laudably to the point Vine seemed a bit overawed by his ennobled guest, at one stage whimpering a half-audible, “That’s not what I said!” and later letting Lord Strathclyde assert, “We’ve seen the head of the Ministry of Defence accuse the Prime Minister of lying,” without qualification.

A pre-filmed package on MPs’ salaries and allowances followed, and this was unashamed knockabout fun bolted highly successfully onto a serious message. Max Cotton paraded around London with a large cardboard cut-out of an MP in order to explore the content of the so-called Green Book, a secret document detailing how much politicians are allowed in expenses. Cotton took his plywood friend shopping for digital cameras, ordered him some pizza, then finally handed him over to be hung up in a dry cleaners, followed by the unfortunately predictable remark, “Are we all still being taken to the cleaners?”

The whole sequence worked because Cotton had enough panache and confidence to overcome the lapses into cliché and occasionally preposterous stunts, thereby leaving the viewer profoundly enlightened as to the financial practices of Westminster. A later report on supermarket waste was less effective thanks to correspondent David Thompson letting the paraphernalia – “prop” foodstuffs emblazoned with statistics, an encounter on a park bench between two opposing spokespeople with Thompson squashed in the middle – somewhat overwhelm his presentation.

Half way through the programme we had the regional opt-out, in this instance handing over to the sun-filled foyer of New Broadcasting House looking out over a blustery Oxford Road in Manchester. Previously existing as a separate show on BBC2, now elevated to BBC1 but with its running time halved, this was a smoothly handled transition from national to local concerns helmed by an avuncular Jim Hancock. The 15 minutes slot included a business trip to Prague, a three-way studio debate, and intriguing news of erstwhile Five’s Company host Esther McVey and her attempts to become Conservative candidate for the constituency of Wirral West.

The remainder of the programme was spent back in London, including Jeremy Vine cueing in a report on the New Deal for Communities and handing over to Amanda Parr in Bristol with a cheery, “Amanda, how’s it going?” to which a ruffled Amanda replied, “Pretty good. Pretty windy here, actually, Jeremy!” The whole programme ended with a jolly MP’s quiz, involving a politician being asked five questions about their constituency by textbook “colourful” local residents. Mike Hancock, Liberal Democrat MP for Portsmouth South, got 4/5 – a “great score”, according to Vine – after interrogation by, amongst others, an old woman sitting in a football ground and a lady dressed as a Victorian spinster.

With its undisguised potpourri agenda, supported by a well paced and deftly produced mix of studio-based and location reports, The Politics Show gets away with delivering this sort of survey of diverse viewpoints and issues. Weaker items or those not of personal interest are quickly dispatched – there’s always something new along in a few minutes. The tone is efficient yet welcoming, with Vine deploying his patented amiable mix of inquisitiveness and enthusiasm. Best of all, he doesn’t look like he’s trying too hard, or act like he wants to make viewers grateful for selflessly giving up his weekend to come and hold the Government to account.

After decades of Sunday lunchtime telly resembling a noisy kitchen with all the pots on the go and an atmosphere dripping with perspiration, someone’s finally opened a window.