In reply to pec:
This is the best advice on the thread so far.
OP - that's great you want to get out to the bigger mountains! One of my fondest memories is seeing the sun rise over the mountains on my very first alpine route (I think there might be a photo of it on my profile). It's magical.
You say you want to find partners, but what you really need is experience. Sport climbing is wonderful, but it is designed to minimise risk as much as possible. Whereas much of alpine climbing is about knowing how to manage the ever-present risk.
While courses can teach you the technical knowledge for climbing as safely as possible in the mountains, only experience can help you make the correct calls in a given situation.
(Personal note: I remember, many years ago, being in a white-out snowstorm on Crib Goch in the middle of winter, shepherding a less experienced group who were getting a bit scared. A less experienced me might have been a bit worried; and yet I was humming contently to myself. I knew we all had the right equipment, and I knew exactly where I was, where and how far we had to go, how difficult the terrain was, and what any potential escape options were. And, crucially, I was confident in my abilities, and the abilities of the rest of the group. We ended up having an amazing day out!)
So my advice would be for you to get out into the mountains (in the UK) as much as possible, regardless of weather forecast, and in every season. The UK has a marvellous selection of classic trad mountain routes and summer and winter scrambles. They are also closer and easier to get to than the alps. And in general a whole order of magnitude less dangerous.
A good way to get into this is via a club (your profile says you're based in London, so you might try the NLMC - http://www.nlmc.co.uk/). By doing so you will gain a lot of the requisite experience, make some new friends, and almost certainly find partners for your ambitions in the alps.
Of course, the other way of doing it is trial-by-fire approach: turn up at the campsite in Chamonix and fake it til you make it. Plenty of people have done this too! It wouldn't be my choice, but it's your call.
Best of luck!