If you’re arriving by air then you’ll probably fly into either Grenoble, Lyon or Geneva. The following transfer companies offer airport transfers, either private or sometimes shared:
3 Valley Transfers
Snowbound Transfers to Meribel
Snow White Transfers
There are buses from the airport but you will need to change at Moutiers and they’re not cheap so if there is a few of you it often cheaper to share a transfer.
The train is the cheapest option from the airports but again this will involve several changes and the trains are somewhat infrequent.
It’s about a 9hr drive once in France to reach Méribel. The benefits of driving are no luggage restrictions and the option of an extra day skiing during a week’s holiday but the tolls can be quite pricey on the motorways so something to consider.
The Eurostar offers overnight trains direct from London St Pancras to Moutiers (about 25mins from Méribel, at the foot of the mountain). If you don’t mind overnight travel, and can sleep on trains (or are willing to forego sleep) then this can be one of the cheapest and most convenient ways to reach the Alps. Plus, no extra charge for ski carriage. You just need to be able to carry all your gear!