Sam Sifton, the food editor of the New York Times, sends out an email newsletter a couple of times a week. Not to be harsh, but I find his style a little precious. In a recent dispatch, for example, he talked about a roast chicken recipe which is so good that, he predicts, “it’s all anyone in your set will be talking about in coming days.” I don’t feel like anyone has had a “set” since the 1950s.
Then there are the Britishisms — two in a mere 699 words. He writes, generously, “We are standing by if something goes pear-shaped with your cooking or your [Times] account.”
Elsewhere, he notes that he and his colleagues are accessible on social media. For example, “We swan around on Facebook.”
“Swan around” was a new one on me, but it had a British feel, akin to “lark about.” And British it is. The OED definition for the verb “swan” in this context is: “To move about freely or in an (apparently) aimless way (formerly, spec. of armoured vehicles); hence, to travel idly or for pleasure. Frequently with about, around, or off. slang (originally Military).” All the citations are British, starting with the first, from The Daily Telegraph, in 1942: “Breaking up his armour into comparatively small groups of..tanks, he began ‘swanning about’, feeling north, north-west and east for them [sc. British tanks].”
The most recent is from Dirk Bogarde’s 1980 novel A Gentle Occupation: “She swanned about at the party like the Queen Mother.”
The expression found its way into American English not long after that. Times columnist Maureen Dowd wrote in 1996, “There are a slew of books about making newspapers more civic-minded and a slew of ideologues and burnt-out journalists swanning about, calling themselves journalism experts and reformers.” (Note also the British “burnt” instead of American “burned.”)
In his 2000 book Kitchen Confidential, Anthony Bourdain wrote of a hypothetical dilettante restaurant owner: “He wants to get in the business — not to make money, not really, but to swan about the dining room signing dinner checks like Rick in Casablanca.“
By the way, “swan about” sounds more authentically British to my ears, but according to Google Ngrams Viewer, “swan around” has been more commonly used since the ’70s.
There have been a couple of dozen other examples of both versions in the Times over the last two decades. Even so, I don’t think it will catch on in my set.
notoneoffbritishisms.com 
This sequence from Monty Python is actually entitled ‘Close Order Swanning About’ although the many people who have posted it on YouTube have given it other names.
Not very politically correct, I’m afraid but it went down well in the ‘70s.
That sketch was the first thing that came to my mind, too.
I think swanning around (or about) is not just moving around in a leisurely way, or for pleasure. I think it has a slightly ostentatious nuance to it, meaning moving around and being seen to move around in a leisurely way, like a swan swims around leisurely, and is seen to be clearly doing so.
An American, I’ve always thought “swanning about” indicated a degree of showing off, because…well, swans do seem to know they are gorgeous!
Good eye and ear, Ben!
The Dirk Bogarde quote points to somebody acting above their station. In Britain you see “swanning around like they own the place”
That’s the main usage I experience. Often used in a mixed metaphor: swanning around like Lord Muck.
Mmmm. Pace Python, my interpretation of it is to move around aimlessly with no fixed purpose – just possibly rather beautifully, depending on one’s feelings about swans. I don’t think the ‘ostentation’ is criterial, and the Oxford Dictionary (not OED) definition is right, IMO, in giving three options: ‘move about or go somewhere in a casual, irresponsible, or ostentatious way’.
I remember being somewhat stung in my youth when told I couldn’t go on ‘swanning about’ as a friend put it, with my relaxed attitude to my job at the time. Since then, nobody in my ‘set’ has ever used it.