The Black plug coming out of the inverter is essentially a 240V AC to 5V DC transformer, so what you're doing (if my memory isn't as fuzzy as it should be this time of year) is converting from DC (battery) to AC, then back to DC.
You should be able to find some type of battery that will do the job directly without inverter or black power plug, ie, battery directly to MP3 and speakers.
5V might be a little hard to find, and you will need to cut the wires off of that black plug to go directly to the battery.
If you're not concerned about frying the speakers and MP3 player, try a 6V dolphin torch battery. I doubt it'll be too much voltage and expect it should work, but

I reserve the right to say I told you so.
I'm also happy to take praise if it works
