ACS712ELCTR-30A-T never changes output with changing load
The datasheet contains a graph for &quot;Output voltage versus Sensed Current&quot;.

It shows the output voltage as VCC/2 (2.5V in this case) when no current is sensed.
It also shows the output voltage will increase when sensing positive current flow and decrease when sensing negative current flow.
Your 240V mains current will alternate direction 50/60 times per second. The output voltage of this IC will follow this, going above 2.5V and below 2.5V at the same rate.
The measured current is AC, and it is superimposed on the fixed 2.5V DC level.
This is done to ease interfacing with other devices, such as A/D converters. Most of these devices cannot handle negative voltages. By adding a DC offset the voltage never goes negative, you can then easily remove the DC offset in software.
Your multimeter set to DC voltage measurement will ignore the AC portion of the output and only read the 2.5V DC offset. When set to AC voltage measurement your meter should only display the AC portion of the output and ignore the 2.5V offset.
A oscilloscope would help in clearly displaying what is going on.