Looking at Country Walking, they (and apparently Wainwright) say the SW ridge up Kirk Fell is the steepest mile in Lakeland. Looking at the OS map, it gains about 600m at quite a gradient before easing off for the last 100m. Does look pretty steep to be fair. Not done it myself.
Anyone know of any contenders?
I’m not familiar with the Highlands, and there might be harder slogs there, but I think the SW route up Pen yr Ole Wen in Snowdonia probably gives that a run for its money, if not exceeds it - it’s unrelenting for the first 2/3, not to mention loose.
I suppose there will be steeper sections of paths (and a lot of scrambles), but it’s a sustained steep gradient that really takes it out of you.