The itinerary lasts 12hrs 55min, and has 4 steps, and it will cost 71 euros minimum.
Marseille - Paris
The step from Marseille to Paris lasts 3hrs 20min. You'll travel in a high-speed train.
Paris - London
You probably already know this, but as of today, Eurostar is the only train company connecting France and Belgium to the United Kingdom via the Channel Tunnel.
As for fares, I recommend booking at least a month and a half in advance if you want to find a round-trip ticket for under €100.
Another important point: since the United Kingdom is not part of the Schengen area, passport and security checks can take quite a bit of time. It’s recommended to arrive at least an hour before departure.
The step from Paris to London lasts 2hrs 30min. You'll travel in a high-speed train from the company Eurostar.
On board, you'll have access to: Wi-Fi.
London - Holyhead
The step from London to Holyhead lasts 3hrs 50min. You'll travel in a train longue distance from the company Avanti West Coast.
On board, you'll have access to: Wi-Fi, Drinks and snacks, Bike.
You can find tickets from 27 euros if you book 2 months in advance.
Holyhead - Dublin
The step from Holyhead to Dublin lasts 3hrs 15min. You'll travel in a ferry.
On board, you'll have access to: Drinks and snacks, Bike.
You can find tickets from 44 euros if you book 2 months in advance.