Hi Susan. It seems you've done most of the research to be done on this pattern. Its name is, indeed, "Chinese", and it appears the only company that used the B.P. Co. mark was Brownhills Pottery. We don't have this pattern in the database, only a "Chinese" pattern that is part of a series of children's plates featuring different nationalities - Chinese, Japanese, Turk and so on. Hard to narrow down the date of your plate's production as it could have been at any time during the Brownhills Pottery's run. Also difficult to know how rare the pattern is, though as we don't have it in the database yet it may not be particularly common. Sorry I can't tell you more!