Best options for Eurostar travel between London and Paris?

[Adam B]

My wife and I are flying into London on separate flights, and wanted to take the Eurostar to Paris that same day. Everything that I see on the web site indicates that tickets are non-refundable (translation: You miss your train...tough luck). I know that I can pay a lot more to have refundable tickets.

I'm wondering if we are safe to simply arrive in London, head to the train station, and book our round-trip on the Eurostar then? Or are there provisions in case one of our flights are delayed and we miss a scheduled departure? Are there usually plenty of seats available if we wait until we get to the station to book?

Help!