EDINBURGH—If Scottish nationalists win independence from Britain in this week’s referendum, they will owe at least some thanks to an unlikely ally: the late, former British prime minister Margaret Thatcher. The current Scottish referendum on independence, coming down to a too-close-to-call finish on Thursday, has reignited the fire under Scotland’s long-standing resistance to Conservatism in Britain, especially the Thatcher brand of the 1970s and 1980s. “I came over to independence as a result of Thatcher,” says Douglas Campbell, a 65-year-old Yes campaigner who showed up at a canvassing push near Scotland’s Parliament in Edinburgh on the last Sunday of the...