I know a gent who's done the "Lands End to John O'Groats in a day" thing a couple of times to raise money for charity.
He reckons that for safety reasons it's necessary to take motorways most of the way. To avoid them is to end up with a day so long the risk of accidents becomes too big.
If you then do the vast majority of the run on motorways, you end up with squared off tyres, so add in a fresh set of tyres to the overall cost...
So, with that in mind, I personally wouldn't attempt it in a day - but I might consider it over a week, however frankly I'd rather go tour the Alps for a week, that strikes me as a better use of a week on the bike