LONDON — With nine days left before Britain votes on whether to remain in the European Union, the possibility of Turkey’s becoming a member of the bloc has inflamed the debate, injecting divisive issues of race, religion and tolerance openly into the campaign.

Supporters of a British exit from the European Union say allowing Turkey in would leave Britain exposed to a new wave of Muslim immigration and more vulnerable to Islamic radicals. While Turkey has been pushing for membership, it faces considerable hurdles, and its entry, if it ever happens, would be many years, if not decades, away.

The debate over the vote, which has split Prime Minister David Cameron’s Conservative Party, has largely played out around fear so far. Those in favor of remaining in the bloc, including Mr. Cameron, have emphasized the economic risks of a vote to leave.

Those in favor of leaving, including other leading Conservatives, have stressed the social, cultural and economic risks of continued immigration from other European Union countries, whose citizens are entitled to live and work in Britain. Most of the recent European immigrants to Britain have come from Poland, the Baltics, Spain and Greece.