Stuck on London?

There are also possibilities to get to Lille:

Unless you’ve got a 1st class pass, going via Lille is your only option to make it to Barcelona then.

Option 1:

• 45 min in advance for security and passport controls
• Eurostar London St. Pancras - Lille-Europe 07:04 - 09:26 30€
• breakfast
• TGV Lille-Europe - Lyon Part-Dieu 11:01 - 14:00 10€
• AVE Lyon Part-Dieu - Barcelona Sants 14:35 - 19:34 10€ (+ 2€ fee through eurail.com*)

Option 2:

• Eurostar London St. Pancras - Lille-Europe 30€
• breakfast
• TGV Lille-Europe - Nîmes Pont du Gard 11:01 - 15:27 20€
• TER Nîmes Pont du Gard - Nîmes-Centre 16:00 - 16:09
• break
• TGV Nîmes-Centre - Barcelona Sants 17:46 - 21:29 25€

Do not wait to book. Feel free to ask anything. Use Rail Europe for Eurostar/TGV (no fees) → https://www.seat61.com/interrail-and-eurail-reservations.htm

Eurostar has a passholder quota and summer weekends are extremely popular. Usually sells out weeks in advance.

*Rail Europe does not work for that route at the moment it seems.

Change language to English, then it will work. (Yes, it's a bug.)

There's also option 2a:

Lille Flandres 11:12 - Paris Nord 12:19 €10

Paris Lyon 14:42 - Barcelona Sants 21:29 €35

Alright. I knew about the bug so I switched from French to English to no avail. Looks like you must enter the website in English directly or else it doesn't work.

Hopefully it is fixed very soon.

The UK being surrounded bij water, there are also ferries to get off the island:

you could go to Newhaven on the 20th and take the night ferry leaving at 23:00 for GBP31. Arrival 05:00, short walk to the train station and then take the train at 08:02. With changes in Rouen, Paris and Valence, this will get you to Barcelona at 19:34. There is a later direct train from Paris.

There are more ferries but I used this one as it is connected to rail at both ends *and* it has overnight crossings. 
Enjoy your trip!