Nabila Nanfuka, 22, of Neasden, north-west London, died in Lava and Ignite in St Peter's Street in the early hours.
One witness, James Adetula, 21, said a "stampede" had begun as people made for the exits when they were told that their buses were leaving.
The number of people in the club is unknown and is under investigation.
Supt Andy Cox, of Northamptonshire Police, said they were aware of large numbers of people at the 1,600-capacity venue.
Officers are also looking at whether the club's fire alarm was activated before the crush, he told a press conference.
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