You can't replace the 2 fuse type original fuse block with a single system.
As others have said there are 2 circuits.
1 Circuits supplied with power all the time.
The supply for this comes directly from the battery terminal on the starter solenoid.
2 Circuits controlled by the Ignition Switch.
The supply for these comes from the ignition switch and is only alive when the ignition switch is ON.
If you have connected everything to the one incoming supply without dividing the circuits into permanent supply and ignition On supplies then you are in trouble. You can't turn circuits OFF that should be supplied via the ignition switch.
You either need to divide the fuse box somehow or better still use 2 fuse boxes.
1 for circuits on all the time such as horn and interior light
2 for all other circuits controlled by the ignition switch.
Note that lighting circuits are not fused on most Minis but there is a fuse hidden away behind the dash somewhere that I think supplies the tail lights on Clubman cars but I'm not 100% sure on this as the wiring diagram is unclear.
Regards
RonR