The survey taken at polling stations across the UK suggests the party could get 314 MPs when all the votes have been counted after Thursday's poll.
Labour would get 266, the Lib Dems 14, UKIP none and the SNP 34, the NOP/Ipsos MORI poll for BBC/ITV/Sky suggests.
The pound fell sharply in value after the exit poll was published.
Early results are suggesting a swing to Labour - but it is too early to say whether the exit poll is accurate.
