I have read (no source at hand though) that that one used to be "Nor-itch" but during the 20th century the pronunciation was gradually forgotten and replaced with a spelling pronunciation. If I remember correctly the same was true of Warwick ("War-ick") Rhode Island.
Same thing happened with Berkeley in the US: originally "Barclay", and still pronounced "Barclay" in the UK.
Those wacky Nutmeggers (who badly need a standard demonym by the way) also pronounce their local Thames River as thaymz and yes that's with the th as in thick. But they do pronounce Greenwich (CT) as the English do.