YouGov said the uncertainty around the model was such that it was possible no party would win an overall majority.
"Based on the model we cannot rule out a hung parliament," Anthony Wells, YouGov's director of political research, said.
Sterling fell by around a third of a cent against the US dollar after the news.
Financial markets fear that a hung parliament would extend the uncertainty over if or when Britain will leave the European Union, which it is currently due to do on Jan. 31, depressing business investment and consumer sentiment.
Earlier on Tuesday, a similar forecasting model from a smaller market research company, Focalpoint, showed Johnson on track for a 24-seat majority, down from a majority of 82 seats predicted last month.