Picking up the soup bowl was acceptable in earlier times in England (sources aren't clear when exactly but this must have been true before the eighteenth century because soup spoons didn't exist before then in the West (according to wiki on soup spoons). There is a lot on etiquette in the 1800s in Knife, Fork, and Spoon Etiquette in the 1800s - you mustn't blow on the soup, only use a spoon, don't pick up the bowl, don't slurp, don't ask for two helpings, leave your spoon on the soup plate - but nothing about tilting the bowl.
Then there is a source from 1879 (John H. Young , “Our Deportment”, it's quoted in Etiquipedia) which says you should not tilt your bowl to get the last spoonful. Next, an 1897 source says you could tilt the bowl but it should be away from you. This was to make it clear you were eating the soup, not drinking it (this is according to a 1897 source which is mentioned in this book chapter: web.stanford.edu).
Culture and the company and the social setting usually say what we can or can't do, so I don't think it's possible to come up with just one answer. The design of Chinese soup spoons makes it impossible to get even close to emptying the bowel without tilting (sort of in line with one of the comments above).