Sorry David, not the beach at Blackpool - Southport or Pendine were the beaches used in Britain for LSR attempts
It even says "South Promenade" on the headline. . .
Judging from the Google map there is a straightish bit of about 3000m finishing just North of the tower with a reasonably fast RH bend approaching the South end.
There was enough distance for "standing" mile runs, but for the "flying" records they would have needed a good long acceleration distance. Since there were grandstands at the Finish, it would have been important to finish all the runs in the same place, so they must have worked out that kilometre records would fit and mile would not.
These days we would have a startline and two finish lines at 1 km. and 1 mile and time each run for both distances.