Extra job whilst on furlough 80% salary

Toble

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, 

General_Grant

I suggest you read through the various threads in the coronavirus area of the site.  Right at the top of the Forum page.

Jenna_Appleseed

Dedicated MSE Coronavirus support and help sub forum https://forums.moneysavingexpert.com/categories/coronavirus-support-and-help