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....
And so it begins...
rab - Right, so starting at Mansion House, and getting to MC in 5. Let's see...
1: Moorgate -- Ah, that's closed the diagonals. So we can't start this way... maybe someone else wants to give it a try.
Kilydd - Can the first move be 1 I would suggest that we strat at 0, however, seeing as you speculated as to the first integar. There is doubt as to whether it now can follow that n=2. Pimlico invoking Flach.
Graham III - I would personally look at 1. Kew Gardens, which tells me we need to solve some pretty tough integrals to get any further, but which aren't impossible. String theory might also prove helpful.
rab - ...giving 2. Kensal Rise. Feels good so far.
Blob - 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
Graham III - [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.
rab - 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?
Kilydd - rab] It is possible
Lancaster Gate4 + Willesden3 =
5:East Morington Crescent
There appears to be iterference from at least one curve possibly the Circle.
Blob - No, no, no

         Goodge Street4+Bank3=        6. WestMornington Crescent

Simplicity itself.

Audience - *shouts, screams, generally goes wild for Blob*
Blob - Six ? Six ! I meant 5
rab - Oh, that was simple. Bit of a let-down really.
Blob - Sorry.
Graham III - 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?
PaulWay - Well, 1. Hammersmith with a Zones 1-6 Travelcard is the logical first move.
Badger - Fnweek!
Scuty - What is it about.
This is the end of the line. There is no more.