Paris to London Plane or Train

Where are you starting from, ie in Paris or off a flight arriving in CDG?

If you want to go airport to airport, then fly. If you want to go city centre to city centre, then take the Eurostar.

If you are already at the airport, then I would fly. If you are in the city center, I would take the Eurostar.

You may be able to get a cheap flight but, especially if it's on a small carrier, do check to see which departing and arriving airports you'll use, how to get to and from them, how much it will cost, how much time to allow, and if there are tight luggage restrictions. You may be able to book an inexpensive flight close to your departure date.

If you book the Eurostar ticket right away when it's released, you can usually get the cheapest fare. Note that like an airplane ticket, this is a non-refundable (unless you buy the more expensive refundable fare) ticket to be used on a specific train. The prices will only go up as you get closer to the departure date.

If you are already in the city center, and need/want to be in central London on arrival, the Eurostar wins for convenience. (Basically, no schlepping to and from airports and dealing with the related hassles.) If you get the cheap fare, it's cost effective, or reasonably so. For many, the train is more comfortable than a flight.

Others may feel otherwise, as may you.

Do remember there is a one hour time change between London and Paris. And only buy your Eurostar tickets directly from Eurostar, not a reseller.

Hope that helps.

Eurostar main website: www.eurostar.com
Current Eurostar timetable is here. There is basically one train ever hour, so you have plenty of choice.
Bookings open 180 days (~6 months) ahead, if you want the cheap fares, book as soon as the bookings open in order to get the cheap fares, which start at £41 each way.
Unless you need to get to or from an airport Eurostar is the obvious choice.

To look at the sort of times, city centre to city centre:-

FLY:
An hour to the airport, be there 2 hours for check in (especially CDG which is huge), an hour's flight, Immigration after landing (30 minutes or more, sometimes much more, maybe a bit less if you are lucky), baggage collection 30 minutes, and an hour into London by Tube if you destination doesn't need a change. Total actual travel time around 6 to 6 and a half hours. Security theatre usual big airport with 3-1-1 bag, shoes off, all the usual stuff.

Eurostar:
15 minutes to Gare du Nord, on many transportation lines, Métro, bus, RER; one hour or a bit more ahead, Border Control before you board the train so no extra time on arrival and no additional queueing, 2:15 on the comfy train with big comfy chairs and lots of legroom (and that's the standard class, even posher in higher classes - no cattle class on the train), access to your luggage on the whole trip, no checking luggage (you tote what you brung), walk off the train at the other end and through the green (Customs) channel without stopping, just downstairs onto a Tube or train or out the door to a bus or taxi, 15 minutes to your destination. Total actual travel time around 3:45. Security theatre - very light. Metal detector, bags through the x-ray, shoes on, no need for 3-1-1.

Frankly, that's why the ferries are going bust and the vast bulk of all traffic between the two cities is on the Eurostar.

But if you have just arrived by plane or are leaving London immediately by plane it makes sense to go directly to your airport by plane.