How to beat the 10 car long Southampton to New York Route in the United Kingdom Map Collection set of Ticket to Ride?
Boiler Lagging and Steam Turbines
The times that I have won against someone who got the Southampton-New York route, I had relied on the bonus points from the Boiler Lagging card (score 1 extra point for each route that you claim) and the Steam Turbines card (score 2, or 3 extra points for each Ferry route that you claim).

Right of Way Also, this is riskier but, you can buy the Right of Way card and lay down your own Southampton route next to your opponents route. This is particularly nasty because you will both be hoarding cards, hopefully of different colours, which will cause serious problems for the other players who will need these cardsto complete their routes.

Equalising Beam and Risky Contracts These cards would certainly help, but I have won more than once against the Southampton=New York player without them.

Rules for Ticket To Ride - United Kingdom