Mansion House to Mornington Crescent is possible in exactly five moves if LV>6.4 and Bank Holiday rules apply. I have a really simple proof for this, but my heart isn't what it waaaaaa....
Well, it was most enlightening none the less. I have an inkling it might be possible in 4 moves from Alperton, but that's likely to be a lot harder... shall we give it a try?