Extra job whilst on furlough 80% salary

Employer shut down, going ahead with the 80% salary for staff whilst doing so (which is much lower than the 2.5k limit, circa 1k)
My question - is there anything to stop me getting an additional job whilst I am off from my career for the next 2 months.
I.e. a supermarket job for say 25 hours a week or something to give me some more income in this time? Whilst still getting the 80% whilst furloughed?
If my current employer says they are happy for that to go ahead? where does it leave me/them in terms of rules etc? Anyone know?
Thank you very much, 

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