actually it wasn't near the english shore at all. The titanic sank a little ways southeast of Newfoundland not too far from the Grand Banks. In another day or two she would have been in New York. Of course, maybe the newfoundland shore wouldn't have fit in the song ;)
As far as the film, I liked it for it's stunning detail in recreating the ship but was rather bothered by the "artistic liberty" taken by its makers. But ignoring the totally untrue or glamourized parts there really were some touching moments that actually happened. The ship's string quartet springs to mind. The only problem with ignoring the untrue parts is that you have to know the untrue parts. Most people don't.
Which happens to be another thing that annoyed me about the movie was that it had the effect of making nearly everyone who saw it a "titanic historian." A large number of people started quoting "Titanic facts" they saw in the movie when much of it is untrue. Speaking as someone who has read and studied the wreck and its leading events, freelance of course, yet still quite extensively for many years the movie made a mockery of history. But, hopefully it did inspire a few people to go out and read the big number of great studies and books about the subject and be enlightened.