Clearly you have some pretty good information about a large passenger-carrying ship arriving in Liverpool on or about March 5, 1941, possibly from Canada.
One suggestion is to explore the excellent ConvoyWeb website (http://www.convoyweb.org.uk/) to see if you can find a convoy arriving in Liverpool about March 5, 1941. At the time there were two convoy series that sailed between Halifax and the U.K., designated the HX series and the SC series. Most of the ships in these convoys were British, as were the escorting warships, and most of the ships carried cargo only rather than passengers (to the extent the records show what the ships were carrying at all).
There was a convoy designated HX-109 that arrived in Liverpool on March 4, 1941, having departed Halifax on Feb 13. However only one ship in that convoy was listed as carrying passengers (plus cargo) and then only three passengers -- and that ship was sunk! Umm, definitely not a match for you.
There were no SC convoys that arrived in Liverpool anywhere near your target date.
There is the possibility that the ship in question did not sail in a convoy at all. As I mentioned in my earlier message, some large, fast passenger ships traveled unescorted, on the assumption, which generally proved correct, that their speed allowed them to outrun U-boats.
ConvoyWeb does list ships sailing independently, with applicable dates and ports of departure and arrival. But unfortunately for you, one has to know the name of the ship in order to find when it sailed, whether independently or in convoy, along with dates, ports and convoy numbers, if any. So Catch-22 if you don't know the name of the ship in which your father sailed.
If the ship was not in a convoy it is more difficult to find it in ConvoyWeb. And if it was a British or Canadian transport ship I did not find mention of it since most of the information to which I have access is for U.S. vessels.
You say you have a letter with detailed information about your father's passage. You might see whether there is an indication that the ship was in convoy or not. (This is something a passenger might or might not notice, especially if the passenger was not familiar with maritime or naval operations.) And keep in mind that the arrival date of March 5 may be the date your father left the ship, not necessarily the official date the ship arrived in port, so the official arrival date might be a day or maybe even two earlier. But the key may be whether the ship sailed independently.
OK, anyway, here's another suggestion. Lately a man named Tony Cooper has been posting messages on the Armed Guard message board. Tony is affiliated with ConvoyWeb and he has successfully helped answer several other inquiries, using ConvoyWeb information. You might contact him and lay out the information you have, plus anything useful that I may have found, and see whether he can help. I don't know how closely Tony watches the message board so you may want to contact him directly. His e-mail is email@example.com.