Well, Dave has hugged hoodies in the past, and is already known to be a musical iconoclast – the first Tory prime minister, for instance, with an affinity for the Smiths. And though Cameron has likely never been to Compton, the gritty area of LA in which NWA's famous track is set, he did join parliament from the PR firm Carlton, which technically makes him Straight Outta Carlton. Most pertinently, Dave's media adviser Craig Oliver is regularly seen draped in a pair of Beats headphones, a phenomenally successful product created and owned by Dr Dre himself. Suddenly, it all falls into place.
Or does it? Dre's visit makes things slightly prickly for George Osborne, who is said to have arranged Dre's trip to Downing Street after meeting the rapper's business partner at a do in Los Angeles. The chancellor has called tax avoidance schemes "morally repugnant". But, awkwardly, it has since emerged that part of Dre's Beats enterprise is structured in a way that allows it to reduce its UK tax bill. Oh George.
Still, Dre isn't the only unlikely visitor to Downing Street in recent months. The country singer Carrie Underwood popped in this summer, though, like many visitors, she was there as a guest of a charity rather than Cameron himself. Last year Pele, the world's greatest footballer, knocked a ball around with some schoolkids in the garden – not far, perhaps, from the flowerbeds where the cricketer turned boxer Andrew Flintoff once relieved himself. Meanwhile, one hopes Dre would have been afforded a less furtive welcome than poor Rupert Murdoch, who was forced, in the name of political expedience, to enter via the back door. Twice.
More generally, it's hard to say how many high-profile visitors check into Downing Street every year. No 10 referred me to the Cabinet Office website – which, while listing official meetings and gifts received by Cameron, does not detail the number of visitors to his residence, let alone their identities.
Nor would No 10 respond to our pressing queries about what Dre and co would have experienced on their tour of Downing Street. "It would depend on who the visitor was, and what the circumstances were," says a spokesman. But we can at least guess: presumably there would have been a five-minute hookup with Larry the mice-hunting cat, the nearest thing Downing Street has to a street-fighting gangsta. Dre might then have had a rattle round what is a surprisingly cramped space for an official residence, perhaps peeking in on the cabinet room; the office of Jeremy Heywood, the head of the civil service; and, if he was lucky, the prime minister's own second-floor flat, where we imagine the pair would have discussed Kendrick Lamar's latest and the problems created by Chris Brown's newest tattoo.
Out in the garden, Dre would have checked out the Camerons' newly installed play area – a slide and treehouse combo that esteemed landscape gardener Sir Roy Strong recently termed "ghastly". Straight outta Ikea, by the sound of things.
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