Police have made a breakthrough in the mysterious death of an English dancer whose body was found in a Melbourne CBD strip club more than three months ago.

The body of Stacey Tierney, 29, was discovered in Dreams Gentlemen's Club more than 12 hours after she died on December 19.

A 33-year-old Ascot Vale man was arrested on Tuesday in relation to the investigation on suspicions of perjury. He has been released pending summons.

The fitness instructor from Manchester had been working at the Elizabeth Street club and was partying with several men who fled after she died on a Sunday night.