To travel from London to Paris and reverse is easy and fast. You have several options to cross the Channel from the United Kingdom to France. Either by direct Eurostar train, by bus (using the Channel Tunnel on a train or a ferry) or a self-organized mix of train and ferry for example via Dover and Calais.
The Eurostar high-speed train is the fastest way to cross the Channel from London to Paris. Buy your tickets online. As earlier you book, as cheaper the prices are. Prices are often the same, it doesn't really matters where you buy. Omio is a good choice, but you can also buy your ticket via Trainline and b-europe.
Interrail and Eurail: the Eurostar train requires a reservation starting from Euro 30 and available via ACPRail or b-europe.
There are frequent bus connections offered by Flixbus and others like for example Ouibus. In general it is cheaper than the Eurostar train, but slower. The bus either use a ferry to cross the Channel or is loaded on a train trough the Channel Tunnel. There are overnight connections available - not that relaxing but you save the price for a hotel or hostel.
Ferry and train
A self-organized mix of train and ferry. Sadly the price for foot-passengers on the ferry Dover-Calais isn't as cheap as some years ago. First you travel from London to Dover, where you change to the ferry (foot walk or bus from the station to the ferry terminal). Then use a ferry to Calais. And again by foot or bus from the ferry terminal to the railway station. From Calais railway station go on to Paris.
It is a long journey. There are as well other ferry connections crossing the Channel.
London to Amsterdam by the Dutchflyer ferry
Have a look at the Rail&Sail offers from London via Harwich and Hoek van Holland to the Netherlands. An overnight ferry is available.
BLOG: From London to Amsterdam with the Dutchflyer
Schedules and more information:
London - Paris
Paris - London