I am a travel in Los Angeles. Taking a transatlantic will be quite expensive. Trains are not that cheap either. No train from Europe to Israel, and you know why.
Ships are going from Athen (Greece) or Istanbul (Turkey) to Haifa.
From London to Istanbul, fugure 5/6 days on the train......plus 5 days crossing the Atlantic and coming back at a later date !!!!
round-trip by on the Queen Mary, or other available from New York to Southampton....approx. $4,000 to $6,000 (Ships do not go to London)
Trains may run you close to $1,000 r/t
Plus add hotel in England and in Turkey for 1 or 2 nights, pretty expensive trip.
Planes would save you time and money and you can do it on short hops, instead of non-stop (ie. NYC-London----London-Vienna----Vienna-Istanbul----Istanbul-TelAviv) all are less than 2 hrs trips, except NYC-London : 6hrs.