An invented name, chosen around 1900 for new houses.
It may come from Baronscourt in County Tyrone, Northern Ireland, an estate of the Earls of Abercorn, with which the Irish-born developer Sir William Palliser may have had connections. Or it was simply chosen as a pairing with Earl's Court, the next stop on the Piccadilly line. Unlike Earl's Court, it is written without an apostrophe.