Hello Louie, The Lancastria was used during WW2 to pick up civilians and forces on one of the beaches in France. A German bomber dropped one and it went straight into the hold of the ship and blew her up. There were some survivors, but it was reportedly well over laden with people. My grandfathers brother in law was in the British Army at this time and he waqs killed. I cannot quite remember the details but it happened approx 1942. I do have information I received from the archives here in Liverpool, I'll have to search for them. What was the shipping line that owned the ships you are looking for. Maybe I can help.
Anyway with regards to Royal Engineers I'm going to locate them using a different search Engine. Thanks for the Information Regards, Maria