I want to travel from the uk to new york by ship departing between august 14th and august 17th.?

Question

Any advice on which cruise/shipping companies provide such a service?

Answer 1

Cunard Cruise line is the one which  has regular service between the UK and NY City.  Here's a cruise that departs on the 13th:  http://www.cunard.com/CruiseItinerary_ta...

There are others in August but you probably will not find one on Cunard that departs in the window you have listed.

Other cruise lines have Transatlantic cruises scheduled at various times during the year but the voyages are typically what are called "repositioning" cruises.  Cunard, on the other hand, has regular weekly crossings.