If you know who funds something it tells you a lot. A glance at headlines when passing a newsagent can tell you a lot, too. It is not necessary to read a paper regularly to know its political orientation. Few people have time or inclination to read numerous papers, so we select from what is available. There are few, if any, left wing ones - as mentioned, the Morning Star is communist, so very much a minority interest, and I had to google to see if the Socialist Worker is still in print (it is, but it is mainly online, with a weekly print edition). The Guardian is Liberal, The Mirror is fairly left, the i and the Independent are centrist, and the others are all firmly right wing.
Bias is one thing - the choice of vocabulary in reportage is one example of bias - and the gatekeeping of which stories are reported as big news and which are ignored or given 'dead donkey' status is another. It is all but impossible to write a news story with no bias at all, as we all have views and news can be very traumatic. When papers use populist jibes and soundbite propaganda however, it is a step too far for many, and I don't think that it is hypocritical to feel a deep mistrust of a publication such as the DM without being a regular reader.