Depends on how hard you want to ride, and where you consider Scotland to start. By the road it's about 700 km between London and Edinburgh. A really fit rider would be able to cover that in two days riding if he's travelling light. Anyone who can take 4-6 hours in the saddle daily should be able to do it in seven days, even when carrying gear. For someone with a bit of experience in bike touring I reckon 4-5 days would be a nice target.
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