Many thanks to all the helpful travellers who responded. After more research, I discovered that I could get to my destination more easily (and cheaply) on the underground.

As a side note, for anyone planning to take the Eurostar and/or TGV -- if you know anyone in Britain who can take mail receipt of your tickets, you can save over $200, as I have. Book using the British raileurope site. (Most of you likely already know this...but another newbie might not)