OK, first you get some friends together (it doesn't matter if they don't have acting experience, you're cool and indie) and stage some numbers and post it on youtube. That'll give you some exposure and let you build a fanbase. Once you have your fanbase, get on kickstarter and find a festival to play at. Once you're playing at a festival, invite all the big producers you can think of to come. If you're "ALW with a Sondheim edge" one of them is sure to bite! Then go to stage doors and concerts and stalk big name talent until you've gotten enough actors who will bring credibility/popularity to your show. Now, get the ball rolling with workshops and more producers and voila! West End!
Good luck! But you won't need it. This is a foolproof plan.