The very best way to travel between London and Paris is the Eurostar train, which gets you from Saint Pancras station to the Gare du Nord, or the other way around, in about two and a quarter hours. I really can't think why anyone would fly unless they were already at the airport or were desperate for a few hundred frequent-flier miles.
I usually spend those couple of hours musing about our first dinner in Paris or our first night of theater in London, but some poor souls have to work and need a place to plug in their computers. Now, there are seat-side power outlets in all classes of travel on Eurostar trains, including the cheapest ("Standard" as it is called), but not every one of those Standard cars is so equipped. Happily, the electricity is not allocated at random: if you know which seat to choose when you book your tickets (easily accomplished on line at www.eurostar.com), you can ensure that you'll be able to plug in your laptop.
If you are booking anything more costly than Standard class (Standard Premier and Business Premier), you have nothing to worry about: there's an electrical outlet at every seat. In Standard class, however, only two cars (carriages in UK terminology) per train have this feature: numbers 5 and 14.
Armed with that knowledge and an appropriate adapter (the outlets are UK and French configuration), you'll be able to make your trip productive -- or entertaining, depending on whether you spend it devising business strategies or watching Twilight movies. (Note that, for the moment, there's no wifi network on board Eurostar trains, but this will gradually begin appearing in 2013.)