I am no expert on Landing Craft, but have more than a passing interest in them. LCM3s where used by British forces at D-Day, but I believe all AFVs landed where from LCTs for British forces. They seem to have been for either infantry landing in the asssult or engineers etc, where either LCAs/LCVPs where not available or they needed stores landing with them. The main differences for British LCM3s from US used ones was the deletion of the mg stations and also addition/improvised armour around the drivers compartment ( I am not up on navy terms) often in the form of padded mattress type sections. The were also painted in far more interesting schemes than US ones, which would make a change. LCM6s where just a LCM3 with a welded section to increase its length, but if you were really adventureous a post war British LCM7 could be made, although I think it would amost be a scratchbuild, but the RAF used them and painted them up a bit more colourful than the Navy. Back to D-Day, I think jeeps and other smaller vehicles would be more likely than Shermans.