"I think the quality of something like the Beveridge, for instance, will have a life of its own"

In this quote, Neville Marriner is describing the quality of the Beveridge, a piece of music composed by him. He is recommending that the quality of the Beveridge will be timeless and will stay appropriate for several years to come. He believes that the quality of the Beveridge will be valued by people for generations to come, which it will have a life of its own. This suggests that the Beveridge will be remembered and valued for its quality, regardless of the time duration or the current patterns in music. Marriner is revealing his self-confidence in the quality of his work, and his belief that it will stand the test of time. He is likewise recommending that the Beveridge will be appreciated by individuals for several years to come, and that it will remain appropriate and significant.