If you happen to have a First Class pass, I see availability from Lille-London on 31st, but not in second class.

It is possible that seats will open up. I’ve seen that happen before, so keep checking. You can’t get on without a reservation.

In a pinch, you can get a ferry from Dieppe or Calais to the UK. Or, of course, fly from Paris-London.

There are also cash fares available on Eurostar Paris-London on Monday evening, but they’re expensive.

Do you have a 2nd or 1st class pass ?

The only Eurostar options I see are :

• Lille - London : 31st 1st class only
• Rotterdam - London :
  29th October 19:28 - 21:57 1st class only
  30th October 17:28 - 19:47, 19:28 - 21:57 2nd and 1st class
  31st October multiple trains

What is your starting point ? From Paris you can easily get a ferry across the Channel (best one is Dieppe - Newhaven), the full journey takes quite long though. Otherwise there is the very convenient Hoek van Holland (Rotterdam) - Harwich ferry : 30% discount with Eurail.

Journey example :

• TER Paris-St-Lazare - Rouen Rive Droite 10:16 - 11:56 1.70€ reservation (available at SNCF ticket machines)
• TER Rouen Rive Droite - Dieppe 12:10 - 12:59
• break + 30 min walk to the harbour
• DFDS ferry 16:00 - 19:00 (check-in closes 45 min before departure) 39€ ticket
• 2h15-2h40 journey to London Victoria (longer than usual due to works)

There are loads of trains from Newhaven Town (3 min walk from the harbour) so just take the first one you can after passport control.

As other choices you have Flixbus but I’d take the train + ferry journey over it. In any case much better than paying 250€ for a last-minute ticket.

Crossing the Channel is quite painful I agree… Do not hesitate for questions. Have a look at this page for ideas (times are not necessarily correct though) : https://www.seat61.com/trains-and-routes/london-to-paris-by-ferry.htm