London to Lyon by train

Making the connection between the Eurostar from London and the TGV to Lyon at Lille Europe has the major advantage of avoiding the need to transfer between stations in Paris; which you'll encounter if you opt for the alternative route via the French capital.
This guide explains how to make the connection in Lille.

However, the cheapest tickets for connections via Lille tend to sell out faster than for the journeys via Paris, so this is usually a more expensive option.

Book Early And Save: Yes

Online bookings open: 90 days ahead

The very cheapest tickets tend to sell out particularly quickly on this route.
The ticket agents listed below will not charge a booking fee when buying tickets for this journey

The search results for the London to Lyon journeys on all of the agents below, combine these journeys via Lille with the alternative connections via Paris.

A plus of booking with Eurostar.com is that you can access a 'Manage Your Booking' facility which enables you to change the seat on the Eurostar, that you will have been automatically assigned when making a booking.
Click on the Eurostar 'train guides’ for more information on how to do this.

The ticketing terms:

If you book Standard or Standard Premier tickets, you can exchange them if need be, to an alternative departure on your booked route; but if you want to transfer your ticket to a new departure less than 7 days before your travel date, you will need to pay an admin fee of £30 for Standard Class tickets, £40 for Standard Premier tickets PLUS the price difference with the new ticket you will be booking.
What's new, in response to the pandemic, is that these £30/40 charges aren't applied if you want to transfer to an alternative departure more than seven days before your travel date.

Business Premier tickets are less restrictive, in response to the pandemic they can now be refunded and they can be exchanged to alternative departures without paying the admin fee, or the price difference.
Eurostar's full ticket terms and conditions are here

Using Rail Passes on Eurostar:

Rail pass users can now pay reservation fees to travel on Eurostar trains, in a similar manner to other international European high-speed trains.
The new rail pass reservation fees are similar to the cheapest single journey ticket prices, but as those cheapest tickets can sell out quickly, it's likely that the rail pass reservation fees will save money.
You can purchase these online with no booking fees via B-Europe - or they ARE now available on the Eurostar website.

Booking in advance is recommended as it's not unknown for rail pass reservations on Eurostar services to sell out days or weeks in advance, there is evidently limited availability per departure.
You can obtain a rail pass reservations without paying a booking fee at Eurostar stations.
However, if you want to do this on the day of travel be prepared to be flexible re: the train you will take.

If you are a UK resident, your rail pass + reservation is only valid if you take a train from the UK on the first day that your pass is valid for and return to the UK on the final day that you will be using a pass.

The Eurostar will arrive in Paris at the Gare Du Nord, but the TGV train on to Lyon will depart from the Gare De Lyon.

This guide explains how to make the transfer between the two stations by RER train.
The London to Lyon tickets do not include the transfer across Paris.

When making a booking, check the connection time between the arrival at Gare Du Nord and the departure from Gare De Lyon.
Most of the journeys have a connection time of between 1hr and 1hr 15mins - which should ensure that you won't be making the transfer across Paris against the clock, though the current final end-to-end journey on Mon-Thurs is best avoided if possible.

The alternative journey options:

You can avoid having to make that transfer across Paris if you take one of the two alternative options for travelling from London to Lyon by train.
(1) travel via Lille
(2) taking the direct London to Lyon train (when it resumes operating).

Though travelling via Paris does have the advantages of:

• more departures to choose from
• and it tends to be cheaper too.

Book Early And Save: Yes

Online bookings open: 90 days ahead

The very cheapest tickets tend to sell out particularly quickly on this route; they're more likely to be available if you can travel on a Tuesday - Thursday, or are happy to set off from London early in the morning.

The search results for the London to Lyon journeys on all of the agents below, combine these journeys via Paris with the alternative connections via Lille.

The ticketing terms:

If you book Standard or Standard Premier tickets, you can exchange them if need be, to an alternative departure on your booked route; but if you want to transfer your ticket to a new departure less than 7 days before your travel date, you will need to pay an admin fee of £30 for Standard Class tickets, £40 for Standard Premier tickets PLUS the price difference with the new ticket you will be booking.
What's new, in response to the pandemic, is that these £30/40 charges aren't applied if you want to transfer to an alternative departure more than seven days before your travel date.

Business Premier tickets are less restrictive, in response to the pandemic they can now be refunded and they can be exchanged to alternative departures without paying the admin fee, or the price difference.
Eurostar's full ticket terms and conditions are here