It seems unlikely, given the time period in question, but I can scarcely imagine a King and his retinue deciding to just walk all that way.
An often forgotten fact about king Arthur is his use of African swallows as long distance messengers and delivery birds, carrying shrubberies and other exotic plants, coconuts included, for an improbably long distance. This is, in fact, the reason they were mentioned in the popular documentary on the subject, which unfortunately merely skims over this vital detail, causing your confusion.
The root to this is the exploitation and oppression inherent in the feudal system. It was TREMENDOUSLY expensive for a North European monarch to outfit his retinue with coconuts during that period just to go marching all over England at the dubious behest of an aquatic female (which is really no sound basis for authority). As shown by his attempted diplomacy with the Knights who say Ni, the bequest of shrubberies and other horticulture was an essential component in a king's relations with feudal lords. Indeed, the offering of such coconuts to his retinue may have been a key aspect in retaining the services of such knights as Brave Sir Robin, the bravest of them all.
Sources: John Cleese, Les Fruits D'Arthur; Eric Idle: Run Away! A history of strategic withdrawals during Arthurian England
The range of coconuts extended much farther north during the Medieval Warm Period
The common misconception of the Arthurian tale depicts King Arthur saying that he lied about finding the coconuts, and instead had been given to him by a bird.
This is false however. Most people forget that the swallows actually had a big role in the coconuts.
See, most people dismiss this since "how can a 5 ounce bird carry a 1lb coconut?" Well, to answer that, you must think about something. What also migrates into warm tropical climates, and can carry large objects, but maintain a suitable air speed velocity?
The bird in question, a duck.
It was a bloody good time to be a used coconut trader, I'll tell you that.
Well, I think its clear from the sources that the Grail Expedition was a politically motivated diversionary measure, in an attempt to prevent the Knights of the Kingdom from getting bored and killing everyone. Such expeditions were commonplace at the time since Knights got bored easily.
Coconuts were always an essential part of such expeditions, along with spam and random insults (which were often used as international currency). The Grail Expedition of 932AD cannot be analysed in a vacuum, it can only be understood in the context of the Unicorn Expedition of 931AD, the Fountain of Youth Expedition of 929AD and the Long Expedition to find Barry a Girlfriend of 926AD. Each Expedition necessarily would have used coconuts as a means of transport, since the hobby horse had died out in England in the previous dynasty from overfishing. The Grail Expedition would just have reused the coconuts that previous expeditions used. Once they'd been released from the evidence locker by the arresting officers of course.
Follow up questions: How silly was camelot really? And what do we think the Black Beast of Aaaarrrrrgghh actually was?
Minor correction: King Arthur lived in 93^2 AD
Sure why not: coconuts wash up on the w coast of Europe all the time, so if they'd been highly valued, there would've been trade in them, and surely a kingdom would be able to amass quite a few.
He would have had to find a way, regardless of the coconut situation. I mean, clearly the French already had a Holy Grail, so they'd have always had that to hold over the English. That prospect was unacceptable to King Arthur, so coconuts or no, he'd have had to launch that expedition. And he would have too, had not been for the arrest and all.
On that matter, what were the French really doing in England?