The formation of theoretical foundations for logical semantic as well as initial stages of the development of basic semantical concepts in the British logic of 19th century is viewed in the paper. It has been shown that in the framework of this logical tradition has appeared, first, the principal concepts of the naming theory, and, second, the concept of interpretation. The analysis of Whately’s Elements of Logic has led to the conclusion that the specific essential role in logic which Whately attached to language, produced the setting of semantical problems. The basic semantical concept of the doctrines of term and proposition is that of class in Whately, while in the doctrine of argument he had in fact supplemented the concept of class by the concept of formal language structure, the validity of which is independent of the meaning of words occurring. Then the semantical ideas of J.S.Mill has been inquired, in particular the origins and the role of his theory of denotation and connotation, modification of the semantic application of the concept of class in Whately and Mill. It has been demonstrated that Mill was the first who introduced into logic and investigated the descriptive names, and separated the singular propositions as a distinct kind. The development of another component of logical semantic has been traced, which is connected to the separation of formal algebraic structure from its interpretation, as it was in symbolic algebra of Cambridge mathematicians J.Peacock and D.F.Gregory. In particular, the importance of separation of symbols of operations from that of quantities is discussed. The influence of Peacock is traced shortly on the especial features of De Morgan’s logical contribution, as well as implementation of the principles of Gregory symbolic algebra in the foundations of the logical calculus of Boole. Finally, we have stated that the theory of meaning as such has firstly appeared in the logic of Bradley and it was absolutely indifferent to the development of symbolic logic and that B.Russell has adapted and modified that theory to the version of symbolic logic which he found at Peano and Frege.