In reply to edunn:
Well I disagree with almost everything you have said! With the exception of 4 days being too short.
Its true that sometimes people can get good stuff done in September, but they are almost invariably highly experienced Alpinists, who can handle the short days, the colder conditions, the shut refuges and the lack of marked tracks. They normally have good knowledge of what area will be in under late Autumn conditions, typically can ski or handle Alpine mixed well. I also agree with others that Cham is NOT a particularly good place for a first Alpine trip, being crowded, frantic, quite expensive and prone to bad weather, while not having that many straightforward routes to get a feel of what these big mountains are all about.
I think the OP would be better going to a less busy area, further South or East and concentrating on worthwhile routes rather than particular "big name" mountains. The Ecrins and the Engandine are obvious options, though the honeypot areas of the Ecrins can be pretty crowded as well. Also I would NOT go for a first trip so far out of the main season.
It is worth bearing in mind that at least initially, Alpinism will not tax you technically, so ice-climbing ability up to Scottish IV should be ample for anything you are likely to do. For example, this Summer I sort of climbed the North Face of the Brunneghorn, which is given a notional TD grading but the steepest ice pitch was probably no more than 65 degrees, possibly Scottish III for 50m. But the fact that it is in an impressive Alpine setting makes it FEEL far more imposing than in Scotland, though the weather is (normally) better.
I would also very much NOT drive, especially for a short trip. Driving all the way from Calais (and to Dover from wherever you are in the UK), will leave you knackered for several days and below par, just when you need to be in good shape when attempting your first Alpine routes. You will be similarly knackered after getting back to the UK. Driving makes sense for an extended trip, but fly-drive is much more rational for a short visit.
Post edited at 11:57