I've been dabbling with this in blitz games:
1.d4 d5 2.Nf3 Nf6 3.Bf4 Nh5!?
I don't think it's very theoretical, if at all. It's certainly playable.
Here are some of the ideas:
4.Bg3 Nxg3 5.hxg3
Black has played Nh5 and grabbed the bishop BEFORE white has had the chance to play h3 (and meet Nh5 with Bh2). Now, black has the advantage of the two bishops and has not commited himself to any structure. This is so flexible it can be played many different ways (early Bf5, or g6, or Qd6/Nc6/and an attempt at e5).
5. ... c5 certainly looks like a fine move too.
Variation B ...
4. Bc1 Nf6 Draw?
This could really annoy a proper Londoner. Also, if a draw isn't suitable, perhaps 4. ... Bf5, 4. ... c5, or 4. ... e6 are playable. Even in the draw line, 4.Bc1 Nf6 5.Bf4, it is possible to give up the Nh5 idea and play a standard line of the London.
Variation C ...
Again, there is no one standard idea here. The position is very flexible.
4. ... Nf6 forces white to repeat, play a Colle, or try a Queen's Gambit where the bishop on d2 isn't really that helpful. I'm sure other 4th moves are playable for black too.
Variation D ...
4. e3 Nxf4 5.exf4
Again, black gets the two bishops. This time, the pawn structure is very imbalanced however, leading to a lively game. Black has to watch out for a standard kingside attack here with Bd3, Nd2, Ne5, g4, etc (like in the stonewall). Therefore, 5. ... g6 may be the way to go.
I know this whole "system" isn't worked out completely. In fact, I only started playing it to get away from theory. It does seem interesting though.
It's a lot better than my Alekhine-London variation from 1 minute chess.
(1.d4 Nf6 2.Bf4 Nd5 ?! 3.Bg3 d6 4.e4 Nb6 with crazy play)