According to the Metropolitan Police ... a man came to them in April claiming he was sexually assaulted in Westminster in 1996. And we're told 2 other men came forward in February with allegations of sexual assault -- one claiming an incident occurred in Gloucester in 2013 and the other in Lambeth in 2008.

As we reported ... Spacey became the subject of a Scotland Yard investigation in January when an alleged victim went to police claiming he was sexually assaulted in Westminster in 2005. Cops in London were already investigating 2 similar complaints before that.

We're told, just like the Scotland Yard cases, officers from the Child Abuse and Sexual Offences Command are involved in the 3 news cases.

There's also an active criminal investigation in Massachusetts involving a then 18-year-old male. And the L.A. County D.A. is reviewing other allegations.