The vast majority of the British soldiers retrieved from Dunkirk were taken home by the Royal Navy. The civillian vessels were very important in ferrying troops from the beaches to the warships lying offshore, and certainly took a significant thousands all the way back to England themselves, but it was probably less than ten percent of the total evacuated. Nearly all came back on the warships.
History tends to focus on the little ships - and they did their part - but the Navy did hers as well.
the cRAF did their part too though they are usually spoken poorly of by the soldiers during this operation. clouds prevented soldiers from seeing the raf in action and short range fighters had a limited time over dunkirk compared with loiter time for the luftwaffe.
good thinng hitler listened to goering instead of sneding in the panzers.
a lot of frencjmaen were qalso saved during the evacuation. IIRC lightower of titanic fame used his boat in the evacuation.