In general, a caution 'closes' the matter.
If the police later found evidence which slightly changed the circumstances of the same offence, it's unlikely that any further action would follow. However, in some circumstances, fresh evidence might mean that the police would pursue a prosecution for a different offence.
e.g. Someone might be cautioned for common assault after they were found tussling with their victim. If the police later found out that the offender was actually trying to hold the victim down, while waiting for his mates to turn up with a gun to kill the victim, the fact that a caution has been issued wouldn't prevent a prosecution for conspiracy to murder.
It should also be remembered that a police caution is not a bar to a private prosecution or to civil action. For instance, a supermarket company might find out that someone who stole goods from their store has only been cautioned. That wouldn't prevent the supermarket from launching their own private (criminal) prosecution against the offender. They could also seek compensation, from the offender, through the civil courts.
Chris