How to score the Southampton to New York route in Ticket to Ride UK?
Nothing extra. 40 points is the amount gained for a 10-car route.



The progression of the number of points earned per car is roughly linear.

Length  Points  PerCar  Maps
------  ------  ------  -------------------------------
     1       1    1.00  [Common]
     2       2    1.00  [Common]
     3       4    1.33  [Common]
     4       7    1.75  [Common]
     5      10    2.00  [Common]
     6      15    2.50  [Common]
     7      18    2.57  Germany (x4), Pennsylvania (x1)
     8      21    2.63  Europe (x1), India (x1)
     9      27    3.00  Nordic Countries (x1)
    10      40    4.00  UK (x1)




As you can see, getting 40 points for a 10-car route fits the regular progression. It wouldn't make sense for the 40 points to be in addition to the roughly 40 points one would expect to get from just laying down the cars.