Evgenia P is actually older than the records show. She is a mark 1 LCT - the bow shape is quite distinctive. She was built in 1940 by either Vickers Armstrong of Barrow in Furness or by Alexander Stephen's yard in Glasgow. It depends if she is number 1 or number 19 as all other LCT mark 1 have been accounted for.
Later modifications seem to have increased her length and breadth so that she now resembles the dimensions of an LCT mk4.
She is very rare - only 20 LCT(1) were built in 1940/early 41 and these were all sent to the Mediterranean. A further 10 were built in 1941 but these stayed in the UK for training so only 30 mk1 LCT were ever built and most of the 20 in the Med. were lost and never recovered.
In 1941 the mk2 was introduced and the mk3 introduced later the same year.

She suffered the fire on 14/7/2015.
https://www.youtube.com/watch?v=CEuyE9TCY40

EVGENIA P ex-SOKRATIS EASAMIDES
LR has no builder details or original ID.
No clues from propulsion details as she was re-engined after 1947 with a pair from Union Diesel Engine Co, Oakland CA.

When did she suffer the fire?

According to a Greek site she was a Landing Craft Tank (LCT) Mk4

Built in 1944, presumably she was an ex-naval LCT, but which one? Regards.