Hi Adam
There isn’t an official swim (yet - we are thinking of doing one) but you can get together with other members of the OSS and do it yourself… Details of the swim are in my book (Wild Swim), and if you go to the Outdoor Swimming Society group on Facebook & chat to people you will be able to get more information both about the swim, and potentially more people to swim with. You needn’t even wait till summer - one of my first trips around the island was on Boxing Day. Slack, low tide is key - and good weather. And always tell the lifeguards where you are going otherwise people on the cliff may raise an alarm.
There is an around island Burgh race, where people swim, paddle, float etc, I think that’s around September.
It’s a lovely swim - you can see a bunch of OSS people doing it on this guardian film:
http://www.guardian.co.uk/travel/2009/sep/10/wild-swimming-burgh-is…
All credit for finding and braving this swim, and turning it into something so many of us want to do, goes to a local lady, Kari Furre, who had the bravery to do it first & generosity to share her findings.
You can find many other swims on the OSS swimming map - see www.outdoorswimmingsociety.com
All best
Kate