It looks like you have the wrong replacement switch, if you have 4 cores at your switch then the switch you need is a double pole switch.
This type of switch has 4 terminals and is essentially two switches operated by the one pull cord. So that one side will operate the light and the other operates the fan.
The new switch you bought is a two way switch, so i'd see if wherever you bought will exchange it for a DP (double pole) switch.
Take note of what conductor goes where on the old switch before disconnecting it, use bits of tape to identify the terminal markings so replacing should be swapping like for like. I would imagine the switch terminals to be marked C1 & L1 and C2 & L2 or something along those lines.