Lands End <> John o'Groats is a fantastic challenge ride, the whole country in one ride, can be many things, and a badge of honour. But IMO it isn't the best of tours unless you have many weeks to do it. I did it in 11 days + 2 for traveling, not race pace, but nothing like enough time to explore either. Some parts were not ideal cycling, we went East of the Pennines to avoid the urban riding, though it adds a little mileage. Cornwall was a real disappointment, high hedges on all the lanes, so relentless climbing but no views! I'm not dismissing it, it'd be on my wish list if I hadn't done it, but neither would I recommend it as the best British tour.
Most of my touring has been self planned, which is easier now we have so much choice of online mapping, I use cycle.travel. If I choose what looks like a nice route, it'll often turn out to be a part of the NCN anyway and I've done a fair few of those routes. Two I'd happily recommend to everyone are the Lon Las Cymru, which goes the length of Wales and the Pennine Cycleway from the English Midlands to the Scottish border. Both very hilly, but rewarded with fantastic views mile after mile.
Not wishing to be controversial, but this sort of cycling doesn't require an exceptional expedition bike. First time I did the LLC it was on a £300 hybrid and a decade later when I did it with a larger group, we had a variety of bikes from racers to MTB's, they were all fine.