(For information on how to get to the resorts from within Switzerland go here.)
If you are concerned about the ecological impact of your winter sports holiday, you will be interested to know that a typical trip to Davos from London will generate 17kg, 127kg and 116kg of CO2 emissions respectively by train, car and plane (Source: EcoPassenger). CO2 is a gas that contributes to global warming and which is slowly causing more and more winter sports resorts to become unviable. In other words, and by other measures too, the train is the most ecological means of transport for a winter sports holiday. By far.
There are a number of choices for getting to Switzerland by train, but all of them will require you to take the Eurostar service from either London or Ashford. Your likely choice is to change in Paris but Brussels is also an option and soon Cologne will be too. In Paris you will need to transfer across the city from the Gare du Nord to either Gare de L'Est or Gare de Lyon. For Gare de Lyon take the RER line D from platform 44 for two stops. For Gare de L'Est there is a 10 minute walk from Gare du Nord. Alternatively you can transfer to both using the Paris Metro. From Paris you can take a TGV to either Geneva (for western Valais and Vaud), Basel (for resorts in the Bernese Oberland, eastern Valais and the central Swiss Alps) or, on the same train, Zurich (for resorts in the eastern Swiss Alps). You can then transfer on to your final destination via the excellent and reliable local Swiss Railways. It is entirely feasible to have breakfast in London St Pancras and dinner in Wengen, Davos, Zermatt or Verbier - or a choice of dozens of other resorts - with total journey times generally around 10 or 11 hours.
For the 2012-13 season Eurostar have also started an excellent direct service to Valais running every Saturday from 22nd December until 13th April. The train starts early from London St Pancras, stops at Ashford, then switches at Lille to a TGV before the train makes four stops in Valais later the same day, in plenty of time to transfer to nearby resorts. From Martigny, Verbier is less than an hour away by train whilst from Aigle, Champery in the Portes du Soleil, Villars, Leysin and Les Diablerets all less than an hour away. Saas-Fee is less than an hour and Zermatt is almost exactly an hour from Visp. Brig gives access to the outstanding Aletsch Arena, with the resorts at Riederalp and Bettmeralp only 45 minutes away. Return fares start from £189. For more details visit Eurostar or call them on +44 8432 186186.
There are numerous deals for using public transport in Switzerland. There are a number of passes and a transfer ticket that are only available before you come to Switzerland for travel within the country - details here. Probably the best value once you are in Switzerland is the Snow'n'Rail deal which gives you around a 20% discount on rail travel and lift pass. Details are listed on participating resorts at this site or here. In general, trains and buses in Switzerland have facilites to carry winter sports equipment. If you visit Zurich main train station early on a weekend morning, you get the feeling that the whole world is taking a train to the slopes - fortunately, with so many destinations to choose from, those crowds rarely translate into standing room only or lift queues.
Most of the major airlines have flights to the major Swiss Airports of Basel, Geneva and Zurich, including Swiss, Easyjet and British Airways. Flybe operate flights from Jersey and Southhampton to Bern and Cirrus Airlines have flights from Munich and Erfurt to Bern. Snowjet operate the UK's only scheduled ski flights to Sion airport, where the runway is so close to the slopes that you look down on it from some of the runs of the 4 Vallées. A shuttle bus runs to Sion Bus and Train Station from where regular, reliable buses run to Nendaz and Veysonnaz, and trains run to Martigny from where a train runs to the valley station for Verbier.
Some airlines charge extra for ski gear - policy varies so check with the airlines. The only airline that consistently permits you to take winter sports equipment for free is Swiss. If you are not flying Swiss Airways (or even if you are) you may want to consider a service provided by the Swiss Railways to take all your baggage from any airport to most resorts at a modest fee. Many hotels will even pick it up for you, and deliver it to your room. How's that for service! Follow this link for details.
Public transport also usually provides the best way to transfer from your airport to your resort - taxis in Switzerland are not cheap, and the public transport is highly efficient. There are railway stations actually in Geneva and Zurich airports, but the bus transfer from Basel airport to the railway station is a doddle too - although remember to choose the Swiss, and not the French, exit!
If you drive to Switzerland do remember you will need a carnet to drive on the Swiss motorways - they are available at the border or at service stations ahead of the border, will set you back 40 SFr and are valid for a year.
See the Getting About page for more details on using public transport and driving in Switzerland.
I won't list all the travel agencies that provide winter packages to Switzerland - pretty much all of the operators do, although the range of resorts is usually limited to the usual suspects of Davos/Klosters, Jungfrau, Saas-Fee, Verbier and Zermatt. The Getting About page gives drive times to most resorts, although bear in mind transfer times will be longer if your drop-off isn't first.