The French haven’t started the Montpellier - Perpignan LGV, and aren’t likely to do so any time soon!Barcelona is one possible future destination, if the French ever get around to finishing that high speed line from Montpellier to Perpignan, and/or the LGV Nord shortcut via Amiens (LGV Picardie). Paris would be three and a half hours from Barcelona, so you'd be looking at about five and a half hours London–Barcelona.
Also, it would be about 5 hours. It is 1100 km via Lyon; a non stop train from Gare de Lyon would be past Montpellier in about 3h15, and there is still another 350km to go. But the train couldn’t go that long non-stop a) for staffing reasons and b) there isn’t the market for it; it would need to stop for traffic (as the current Paris - Barcelona services do)