This is a map showing all land over 2,000ft in Scotland just because @VictimOfMaths asked for it and because we need to know 'what's the longest distance you can walk above 2,000ft in the UK?' and suchlike

here's that high land as islands

and here's what we might call 'Munroland' - everything 3,000ft or above

PS 2,000ft = 610m and 3,000ft = 914m and peaks of 3,000ft or higher are 'Munros', just in case you're not into Scottish mountain lingo or the imperial system of measuring the world

and the first and second images above as a looping gif just because I like gifs - so you can see where the land over 2,000ft is in relation to the rest

would need higher resolution data for this to be definitive but it looks like it is possible to walk for more than 50km without dipping below 2,000ft