I may be wrong, but I think that the word "nursing" is American
rather than British usage. I'm English, and before I encountered La Leche
League, the word "nursing" summoned up to my mind a picture of hospitals and
invalids.
        Having said this, however, you may like to know that "to breastfeed"
is the original meaning of the verb "to nurse", while the noun originally
meant "wet-nurse". According to my little etymological dictionary, the noun
came into English from the old  French word "norice" which goes right back
to the Latin word "nutricia" meaning "wet-nurse". (A lot of French words
came into English after the Norman conquest - if that hadn't happened, the
language would now look more like German or Swedish.) The original source of
these words is the Latin verb "nutrire": "to nourish".
        If anyone wants to trace the history of these words in English, you
need to get hold of the Oxford dictionary - not a little one, but the full
version, which consists of about 20 huge volumes, and traces the history of
words, with examples, back to the Middle Ages.
                                Anna Lowenstein, Zagarolo, Italy