Well from what I remember it was not public knowledge that the Lusitania was carrying war materials and I seem to remember Britain denying she was carrying any.
You're confused. Britain denied the liner was carrying contraband, not war materials, and Britain's denials were in direct response to German "spin" efforts to justify the sinking after the fact.
From the war's beginning, both sides had dozens of public relations flacks at work in the US. They'd give speeches, make press releases, and engage all the usual kinds of "spin". One of Germany's better PR flacks was a Dr. Dernburg. He was a former government official and gave a speech at some midwest club on May 9th, 1915 - only two days after the sinking - justifying the sinking with the contraband excuse people are still innocently quoting today.
In reality and IMHO, Germany didn't need to justify a thing.
Pick up
"Lusitania Saga and Myth" David Ramsay. It rather exhaustive and should prove quite an eye-opener for you.
What I meant was the officially Britain says to the public she was not carrying explosives...
Britain can't do that because the public in the shape of the manufacturer who sold them, the railroad who carried them, the stevedores who loaded them, and the port officials who cleared them, would have known she was carrying explosives. In order for any ship to be cleared for departure, a federal government official known as the Collector of the Port of New York has to sign off on a ship's cargo manifest.
Lusitania's manifest was and is a matter of public record and, because the numbers of US workers that would have been involved, there is no way that a significant amount of explosives could have some how been sneaked or smuggled aboard.
What the liner was carrying was public knowledge. The only point of contention immediately after the sinking was whether what she was carrying was contraband or not. Sadly over the decades the original "contraband" question has been conflated into a "war materials" and too many people now seem to think the
Lusitania was carrying kilotons of artillery shells rather than a few thousand rounds of pistol ammunition and leather belts.
She would have been chosen because she was fast and making the route already and as a passenger liner less likely to be attacked
Pick up the book I already mentioned and read why none of those "reasons" really holds up.
If
Lusitania had taken on a load of explosives and those materials exploded while she was in port, public opinion and official condemnation would have fallen on the US port officials who allowed those materials to be loaded aboard a ship not designed to carry them and for the lading to occur away from the already designated explosives piers/anchorages.