The easiest, although not necessarily cheapest, way would be as follows:

1. London Waterloo to Lille Europe Eurostar
2. Lille Europe to Nantes TGV
3. Nantes to Vannes TGV
4. Vannes to Carnac by the power of the thumb

BUT...to be really honest with you, unless you at least had push-bikes, you'd be missing out on a lot of stuff.... HOWEVER if the need takes ya, do it!