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....
Presumably, as Mansion House is not being named as move one, then it is assumed as move zero. In that case do you hypothesise that we should reach MC at move four or move five ? Anyway from Kensal Rise, I feel the only playable jump which is even vaguely in the correct direction is 3. Bank
[Blob] I'm not sure Bank is useful here - you might have missed a negative somewhere, as I don't find anything useful in that avenue... Try applying triple chain rule, and you'll find that 3.Willesden could be more helpful... I haven't followed it through yet though.
To clarify, Mansion House is move zero, aiming for MC at move five. Anyway, I shall try 4. Lancaster Gate, with negative spin. Is it possible from here?