Instructions
Look for marks or back stamps, usually located on the bottom of the piece. There have been several incarnations of Beswick back stamps, making it the best reference because particular markings denote specific time frames for the production of a piece. For example, earlier marks are generally green with "Beswick England" stamped in a circular pattern; pieces after 1954 had impressed markings accompanied by a serial number.
Determine the character the piece depicts or the collection it belongs to for figurines with no back stamp or marking. Because certain collections were introduced in specific years, there is a somewhat reliable timeline to refer to. For instance, if the subject is a Beatrix Potter character, such as Peter Rabbit, that would place its age at no earlier than 1947, the year that John Beswick first secured the rights to use the characters. Likewise, if it is a Disney character, the piece can be no older than 1952.
Compare your piece to other dated pieces online. One way to distinguish one piece from another is to look at the color. Before the prohibition of lead-based paints in the 1980s, the colors were darker. If your Peter Rabbit has a deeper blue coat than those made in the 1980s, then you can infer that your Peter Rabbit is no older than 1947 and no younger than the 1980s.
Seek out like-minded individuals by visiting message boards and collector websites, if all else fails. There are numerous websites that contain information, and message boards discussing everything from dating and appraisal to the buying and selling of Beswick figurines. There is a good chance that the half you know plus the half they know could equal the whole story.