I wish to search for the programme where the name includes "Afternoon Concert" and the episode includes "Live". I don't see how this can be done at present as the search term is ran against all specified fields.

So as to maintain backward compatibility, you could leave things as they are but add numbered search options, e.g. Search1, Search2 and so on, where the number refers to the order of the fields specified in the Fields option.

Example:
fields name,episode
search1 Afternoon Concert
search2 Live

fields episode,name
search1 Live
search2 Afternoon Concert

Sorry, but it's a no from me. Numeric suffixes on the "search" key are already used for another purpose. More to the point, this is unnecessary. Your example can be covered by:
If you don't understand why that works, see the "Searching for programmes" section of the documentation.