The Eurostar check-in closes 30 minutes before departure time. leaving only 14 minutes is cutting it very, very close. It's better to arrive a bit earlier. The best time to join the queue at the check-in is 45-60 minutes before departure; if you arrive before that, just go and have a coffee nearby.

If you arrive early, Eurostar might let you on an earlier train but don't count on it.

TGV reservations can normally be exchanged or cancelled free of charge until 30 minutes after departure time. raileurope.com (or their app) lets you cancel reservations easily. Changing TGV reservations can be done in the TGV Inoui Pro app (only in French), at an SNCF ticket machine or ticket office.

For reference I asked about getting on an earlier train in Lille-Europe: they said “sure” and then “that will be 20€ each”. So don’t really count on it, at least not for free. (In the end both trains were 1h late so we’d have left at our original time anyway...)

As rvdborgt suggested, I’d have a coffee before all the security checks (the St. Pancras terminal is cramped).

Thank you 

You're coming from Newcastle right? Same as me!

It's possible to get the 1024 from arriving at 0940, and I've done it several times, but it's not an official connection. This means if you miss it for any reason, it's your fault, not Eurostar / LNER / Interrail’s.

Don't count on them moving you forward to the earlier train if you book the 1131 either, even for £20. It's not guaranteed.

You can take the risk. But as painful as it is, I'd try and get the earlier train down to London, especially if you have onward connections to make.