It’s easy to get from London to Bruges by train. Trains from London to Bruges run via Brussels and require a change at Brussels Midi-Zuid train station.
To take a train from London to Bruges, first take the Eurostar from London to Brussels. Details on how to do this can be found here.
Eurostar trains from London to Brussels arrive at Brussels Midi-Zuid train station. From there you can change for a train to Bruges, which will take around an hour.
You can take a train from London to Bruges for just £45 each way if you book your Eurostar ticket in advance online. This includes the segment from Brussels to Bruges.