There are quite a few inaccuracies in the report of the French Rail Speed record.
The distance from London to Edinburgh is 393 miles and at 331mph will take take longer than 1 hour (60 minutes) The French are already running at 320 kph (no miles in France) on the TGV Mediterrean Line (320kph = 198 mph) on a short stretch for test purposes, French train drivers are encouraged to use the extra 20 kph (normal speed is 300kph = 186 mph) if running late. 331mph = 532 kph in proper units. BUT I understand that they have reached a speed of 553kph (343 mph) earlier this week but have not made an official announcement. It is anticipated that they will be running faster than 553 kph before the test programme is complete. They are using a very much shortened TGV train set i.e. 2 power cars and 2 trailer cars (4 cars in length) and are using the opportunity to test new equipment and brakes for the next generation of high speed trains being planned although not built yet. Hope this clarifies matters.