This would be 'The Great Triangle (Dover, Lands End, Cape Wrath, John O'Groats, Dover). A free route and start where you like. Reckon on about 3200km so you're well into an easy (!) 200km a day territory if thats your fancy.
Teethgrinder was the last to ride some years back, famously abandoning mid-route because of the weather if I recall correctly, going back to work for a week and then returning to finish it off as he was still within the time limit!
Alas it has fallen off the listings but easily restored...