I think it would be more precise to say "My favourite fruits ARE apples and bananas." and "Apples ARE my favourite fruit." Note that "are" is the plural form of "is". In America, we would spell it "favorite". Written and spoken english would be the same.

If you must start with "My favourite fruit", then the form that I would recommend is "My favourite fruit are apples." By the same token, "My favourite food are oranges." A single subject can take a plural object via a PLURAL noun. For example, My favourite race are the Chinese people. My favourite music are the Bach concertos. I think many grammarians have discussed this, and this seems to be the primary position of Fowler and his ilk. Fowler remains today a major authority on English usage. The book "Fowler's Modern English Usage" is regularly updated by experts at the Oxford University Press. H.W.Fowler died in 1933.