So, when is it OK to take off your shoes?

John Walsh puts his foot down about a lapse in sartorial standards at No 10

"Doth not Brutus bootless kneel?" sneered Julius Caesar, just before the unshod Brutus (and Cassius and a few others) killed him on the steps of the Capitol. He was using the word in its old sense, to mean "fruitlessly", but it still carried a slight ring of contempt about it. How much ridicule are visitors to David Cameron's inner circle allowed to express about the new Downing Street fashion for chaps going about without footwear?

The trend seems to have originated with Steve Hilton, the Prime Minister's characterful director of strategy, a man who is to formality what Silvio Berlusconi is to chastity.

Known to his immediate staff as "Gollum" because of his shaven head and attractive manners, he routinely prowls the corridors of No 10 in T-shirt, jeans and red trainers. He habitually arrives for work on a bicycle in grey singlet and baggy shorts. Last week, he greeted a visiting group of suited entrepreneurs and delivered a speech to them while wearing a white T-shirt and socks – but no shoes.

Instead of dismissing him as a hippy fool, other political heavyweights joined in. Andrew Mitchell, the Government's Secretary of State for International Development, was also snapped last week welcoming the members of an Action Against Aids charity in stockinged feet.

Informality in the courts of power, as everywhere else in British society, has undergone a gradual evolution that seems to have speeded up in the past few years. Until the end of the millennium, no gentleman in power, in business or in public-sector management would have dreamed of wearing anything but a suit, a tie, and some sturdy black brogues over sensible dark socks.

The idea was to join in with the English-gentleman look in order to gain the trust of your peers, rather than to draw attention to oneself as an outsider. But elsewhere in society, things were loosening. Academics took their cue from FR Leavis and wore open-necked shirts. Newsreaders ceased to wear evening dress. Businessmen such as Sir Richard Branson, inventors such as Sir James Dyson, and dotcom millionaires such as Brent Hoberman were all visionaries in blue jeans.

The rise of designer clothes meant that the oik trying to reserve a table in San Lorenzo could be a denim-wearing millionaire, so the owners let him in. From restaurants to municipal halls, the old dress codes were abandoned. When John Bercow, the Commons Speaker, declined to wear a wig, it was the culmination of a brisk evolutionary process.

The shoe-less Joe look is a regrettable lapse of taste for such style icons as Mr Hilton and Mr Mitchell. It suggests not that one is a relaxed, amiable, laid-back and chilled-out kinda guy, but that one has recently risen from an elderly snooze on the sofa. Its main cultural exemplar is Bertram Cooper, senior co-founder of Sterling Cooper, the advertising agency at the heart of Mad Men: he insists all visitors remove their shoes before entering his domain, a piece of faux-Oriental politesse about whose origins even Bert himself seems hazy.

Fans of Mr Hilton may insist that his bracing approach to executive style is meant to suggest transparency, honesty, simplicity. Unfortunately, they're wrong.

When you're tie-less, shirt-less, jacket-less, trouser-less, shoe-less and sock-less, it is quite as likely you'll just seem clueless and pointless as well.